Can I get pregnant if I masturbate on my period?

No. You can only get pregnant if sperm enters your vagina at a fertile time.

1. Unless you have sperm on your hand (or whatever you use) when you masturbate, there is no way for sperm to enter your vagina.
2. Usually, a girl is not fertile when she is on her period.

What did you have on your mind? What is the scenario?

I hope this helps as a start, but if this raises other questions, feel free to ask.