Normal-ish, but you should not pay before getting the terms in writing. A good faith deposit can be legitimate, but it should be accompanied by a signed, conditional agreement that states: the amount, exactly how it gets credited, the deadline for applying, and under what conditions it's refunded.
In practice, it's often refundable if the application is rejected or if the lease materially differs from what you were told. If you're approved and then walk away just because you changed your mind, the broker may try to keep it — so read that part closely.
Always pay by a traceable method to the brokerage, never to an individual agent's personal app. Check the agent's license on the Department of State online lookup, and ask to see the broker's agency agreement if you want to be thorough. Also, a legitimate broker should be willing to send you the landlord's lease form or at least a lease terms sheet before money changes hands. If the answer is "pay first, lease later," I'd be very cautious. I've rented three times in Manhattan and Queens, and each time the good faith deposit was conditional and the lease packet came within a day or two.