Can I still file a 1040 with zero income? My son is a student and needs to fill out a FAFSA for financial aid and it requires verification of a parents income?

No, you would have to mail it in. The program will not allow a return with only zeros to be e-filed.

you must have some income from somewhere even if your tax is zero.

Or does your son support you 100% ?

if you want to e-File an empty return enter one dollar of interest  income.