21st century etiquette says that the host pays the tab regardless of gender. This means the person who asked for the date pays.
Some may prefer to split the cost of a first date so that no one feels indebted to the other person, which is perfectly fine. If you’re worried about confusion arising when the bill comes, you can address the issue head-on when you accept the invitation.
Men, just a side note, from personal experience. “I’ll pay if you put out” should never be part of the conversation or expectation. If you want or expect to pay for services, you need to find a whore, not ask a women on a date.