The SIM card should fit. However the AT&T iPhone might not be compatible with the Verizon Wireless network especially if it isn't unlocked fully.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
It’s important that you can bring your device to our network, SAUNDRA098. As Ann154 mentioned, the SIM cards are comparable in size, but there may be some features that are not available. You can always check to make sure your iPhone will work by checking here: https://www.verizonwireless.com/prospect/bring-your-own-device/#/
Also, if you need a new SIM card, we provide them at no cost at our corporate retail locations and through customer service.
Does this help answer your questions?
Follow us on TWITTER @VZWSupport
If my response answered your question please click the _Correct Answer_ button under my response. This ensures others can benefit from our conversation. Thanks in advance for your help with this!!