Yes! a BCA graduate can take AFCAT exam provided the degree is recognized. If you are selected for GDOC or flying branch, He/She will be eligible to apply for both Ground Duty and Flying branches , you need a graduate degree ( min. 3 years). In your case BCA will do.
You cannot apply for Technical beach as the eligibility is a 4 year degree.
If the person had studied Physics and Mathematics in PU (12th standard) or else he/she will be eligible to apply only for Ground Duty branch.
So in short you can attempt AFCAT. Just check your age requirement.