Sorry ... didn't know I was being paged ... haven't checked the board in a while.
Yep, every Colt I've encountered --- original, reissue or reproduction --- shoots high.
Doesn't matter what the model or caliber, they all shoot high.
The best cure is to put a higher front sight on, as others have detailed.
But before you go fiddling with the sights, find your most accurate load first.
My 1860 Army, made by Pietta and marketed by Traditions, is wondefully accurate. Five or six balls into a 2" circle at 25 yards from a benchrest is not unheard.
However, much of that accuracy comes from properly loading it.
1. Use FFFG black powder.
2. Use balls of .454 or .457 inch, contrary to many manuals that suggest a .451 inch ball. The larger diameter ball, when rammed into the chamber, creates a longer bearing surface for the rifling to grab. Obturation is greatly improved too.
3. Use a well-greased felt wad twixt powder and ball. Melt some lard, Crisco, bacon grease or any other natural grease in a small can and add the wads. Swish them around so they're well-soaked. The commercially available Wonder Wads by OxYoke are okay, but their dry lubricant is not enough, in my experience.
4. Measure your powder consistently with a powder measure.
5. After the powder is added to the chamber, seat the greased wad firmly on the powder.
6. Seat the ball on the wad in a separate operation. This will give you a better "feel" for how much pressure you're applying to the ball and wad.
7. Try different caps. I've had the most consistent ignition and best accuracy with Remington. You may find that CCI or foreign caps work best.
8. Shoot at a well-defined target with plenty of paper around it to display any bullets that go off-course. A 4X4 sheet of plywood at 25 yards, covered with butcher paper, is not excessive.
I have a cheap, badly made 1849 Colt reproduction I bought in the 1970s. Its little .31 caliber balls often can't hit a 4X4 sheet of plywood at 25 yards! If I hadn't taken the time to test it this way, I would have wasted powder, shot and caps assuming that the miss was MY fault.
9. Avoid conical bullets. Never found one yet that is nearly as accurate as a lead ball. I've tried Lee (cast by myself), Buffalo Bullets and a few Lyman designs. Ack! I went back to lead balls quickly enough.