The short answer, before anything else
No. Not reliably. Any calculator, app or astrologer that hands you a confident rising sign without knowing what hour you were born is guessing, and dressing the guess up as information.
That is the honest answer, and it is where most articles on this question stop. Which is a shame, because in practice the birth time turns up far more often than people expect. Most of the people who write to me convinced their time is lost are American, and most of them are holding the wrong document without knowing it: the short form birth certificate that gets issued by default leaves the time out, while the long form usually has it. In England and Wales the problem is the opposite and worth knowing early, since the time was never recorded on the certificate at all and no amount of reordering will produce it.
So the rest of this is about where to look, what your chart can still tell you in the meantime, and what remains possible if the hour genuinely never surfaces.
Why your birth time decides your rising sign
The rising sign, or Ascendant, is the degree of the zodiac coming up over the eastern horizon at the moment you were born. The horizon moves as the earth turns, which means this point travels through the entire zodiac every twenty-four hours.
That works out to roughly two hours per sign on average, and the average hides something important. Signs do not all rise at the same speed. Depending on your latitude and which sign is coming up, one sign might take barely over an hour to clear the horizon while another takes closer to three. The further north or south of the equator you were born, the more extreme this becomes.
The practical consequence is that a twenty minute error can put your Ascendant in a different sign, and a two hour error almost certainly does. And the Ascendant is not a decorative detail. It sets the entire house structure of your chart, meaning it determines which area of life every planet occupies. Change the Ascendant and every planet moves house.
This is also why the tables that circulate online, the ones that promise your rising sign from a two hour birth window, tend to fail. They assume a uniform rise that does not exist.
What your chart still shows without a time
A chart calculated without a birth time is not empty. It is worth knowing exactly how much survives, because people often abandon the whole enterprise unnecessarily.
Everything that depends only on the date holds firm: your Sun sign, the sign of every planet, and the great majority of the aspects between them. Your Mercury, Venus and Mars placements are yours regardless of the hour. Slower planets do not move enough in a day for the time to matter at all.
The Moon is the one to watch. It covers around thirteen degrees a day, so on most days the sign is certain no matter the hour. But if the Moon changed signs on your birthday, the time decides which of two signs is yours, and the difference is substantial.
What you lose without a time is the framework: the Ascendant, the Midheaven, and all twelve houses. You know the cast. You do not know which rooms of your life they are standing in.
Where the birth time is actually recorded
This is the part that tends to solve the problem, and it depends entirely on where you were born.
If you were born in the United States, the time is very likely on your birth certificate, but probably not the copy you own. American states issue two versions. The short form, also called an abstract, is the condensed one most people have in a drawer, and it usually omits the time. The long form, sometimes called a vault copy, is a full reproduction of the original registration, and it normally includes the hour and minute of delivery.
You order the long form from the vital records office of the state where you were born, usually online, by mail or in person. Fees generally run somewhere between ten and thirty five dollars. Request the long form specifically, because the short form is what gets sent by default.
One caveat worth having in advance: practices varied by state and by decade, and a small number of jurisdictions did not use a time field on certain older forms. If your long form arrives without an hour, the record may still exist elsewhere.
If you were born in England, Wales or Ireland, stop looking at your birth certificate. The time of birth is not recorded there, with one exception: twins, triplets and other multiple births do have their times entered, because birth order carries legal consequences. For everyone else the field simply does not exist, and ordering another copy will not change that.
If you were born in Scotland, the situation is completely different and much better. Scottish statutory registers have recorded the time of birth on every entry since 1855. If your birth was registered in Scotland, the hour is in the register, and you can obtain the record through ScotlandsPeople or the National Records of Scotland.
Hospital records are the second route everywhere, and often the best one for births in England and Wales. Delivery notes and labour records almost always contain the exact time, since it is a clinical detail rather than an astrological one. In the United States, health privacy law gives you the right to request your own records from the hospital that holds them. In the UK, NHS trusts handle these as subject access requests. Retention periods vary, so older records may or may not have survived, and asking costs nothing but a form.
Then there is the least formal route, which succeeds more often than any of the above. Baby books, christening records, letters, the annotated photo album, the diary your grandmother kept. Ask family members separately rather than together, because memories contaminate each other quickly once one person says a number out loud. "Just before dinner" and "the nurses were changing shift" are more useful than they sound. Shift changes in hospitals happen at fixed hours.
If the time turns up
Then you are done, and the whole question dissolves in about a minute. You can calculate your Sun, Moon and rising sign for free with the Sun, Moon and Rising Sign Calculator, which will also tell you the exact degree of your Ascendant, and from there your full chart becomes readable.
If your recovered time is approximate rather than exact, it is still worth entering. A time you trust to within fifteen minutes gives a rising sign you can rely on in most cases. A time you trust to within two hours gives you a candidate rather than an answer.
If the time never surfaces
Some birth times are genuinely gone. Records destroyed, adoptions with sealed originals, births at home in places and decades where nobody wrote anything down.
There is a technique called rectification, in which an astrologer works backwards from documented events in a person's life, testing candidate birth times against the timing of moves, marriages, deaths and major turns until one time accounts for the pattern better than the others. It is an old technique and a legitimate one, and it is slow enough that few astrologers take it on casually. It also requires the person to supply a detailed and honest chronology of their own life. Anyone offering to rectify your chart from a couple of details in fifteen minutes is not doing the technique.
Short of that, a chart without a time still holds a great deal. The signs, the aspects, the relationship between the planets and the long transits that touch them can be read with confidence, and that reading is often the one people needed anyway. A full natal chart reading can work this way when the hour is unavailable, saying plainly which parts are missing instead of inventing an Ascendant to fill the space.