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