There is no
perfect sign for "alphabet."
Here are some approaches:
1. Fingerspell A-B-C normally, and then do the letter "S" with a twist in the wrist which represents an "apostrophe 's.'" and would basically mean, "The ABC's" (That twisting movement is similar to the movement you make when biting off a piece of beef jerky--a forward rolling twist. But the location is not near the mouth, it is in the normal fingerspelling location.)
2. Fingerspell the letters A-B-C and then you do the sign for "fingerspell."
3. If that doesn't do the trick, you can spell A-B-C and then drag your finger to the right a couple inches (as if drawing a line in the air) and then sign "Z." That would mean "A through Z," which would be understood to mean, "the alphabet."
American Sign Language University ™ ASL resources by Lifeprint.com © Dr. William Vicars