Here's the full transcript of what the says:
"Did Shawn Mendes have braces?" I had braces for four and a half years. There's lots and lots and lots of photo evidence. I'm sure you can pull up a few.
It's quite obvious that by "pull up a few" he means "you can easily find a few photos on the Internet where he wears braces which can serve as evidence that he used to wear braces in the past." I think this is just a variation of the more commonly used expression to pull something off the Web which basically means to quickly find something online and download it. Here's a simple example sentence:
You can pull the files you need off the Internet.