Originally, the correct form was subscripción; however, over the years, the relaxation of the sound of the b in the consonantic group bs+consonant led to the simplification in the writing of bs+consonant to s+consonant. Both spellings are still used (the RAE lists both spellings as valid), but nowadays the simplified form is the one that is almost exclusively preferred. Some other examples of this simplification are:
obscuro -> oscuro.
subscribir -> suscribir.
substancia -> sustancia.
substitución -> sustitución.
*substraer -> sustraer.
There are cases in which this simplification shouldn't be used:
obstante, cannot be simplified to ostante.
abstemio cannot be simplified to astemio.
Of course, the group bs+vowel cannot be simplified to s+vowel, so it's not correct to write, for example, osesivo instead of obsesivo.