Yep - Its going to depend on the size of the cross arm. If just a 2x4 cross arm into a 4x4 post I would think qty 4 16d galvanized nails would work OK. 3" or 3/5" deck screws would be better. qty 3 or 4 1/4"x6" carriage bolts would be best.
The ultimate strength would be to notch the cross member into the post and use the carriage bolts. That would also look the nicest. Me? I would probably just grab some nails or screws and be done with it.