Can an Iphone 5s with AT&T sim card be switched to Verizon?

I bought a phone from Craigslist and the person said they used Verizon, but when I got it home and popped out the sim card it's AT&T. My sim card from my Android is much bigger and doesn't fit into the tray. Is there any chance of getting it to work? Or did I get totally jibed?

I'm not finding clear answers online so I wanted to see if anyone here knows.