Obviously the best thing is to find a birth time through hospital records; the registrar of vital statistics (called different things in different places, but the nearest government office that collects birth records; Mom's or a relative's memory, or a baby book (of memorabilia.)
Sometimes you can make more progress if the moon changed signs on your birthday. It changes signs every 3 days. You will often feel much more like one sign or the other; or people who know you well can describe your emotional nature as they experience it. This would give you a narrower range of rising signs from which to choose.
Otherwise, just learn to read charts without houses. As indicated above, you can make some progress with traditional astrology so long as you've got planets-in-signs. I recommend using the free charts section at Astrodienst
www.astro.com . Input the birth time as "unknown," and you will get a chart without houses and a default noon birth time. Just recognize that the moon could move 6 degrees in either direction.
Aspects in astrology are awfully important, and you don't need houses to read them.
If you can narrow down your rising sign but don't know it to the minute, I suggest using whole sign houses. The others suggest a degree of accuracy that you wouldn't have.
There are chart rectification methods, some of them very sophisticated, but for these an amateur might best consult an experienced professional astrologer.