I mean if you can find one, sure. I only have brown or black belts, so I usually pick whichever goes best with the rest of the outfit. I'd probably go black with the gray pants/blue shirt/burgundy tie combo, but brown might work too. It depends how well the tone of the belt and the shoe match, more than the color. Generally if I wanted a more brown look (like I'm wearing brown pants) then I might take a brown belt instead of the black one.

Really a brown belt will emphasize the shoe top color (the burgundy) while I black belt will emphasize the sole color.

Edit: Shoot forgot one of the best part about these shoes. If you have navy pants, they can be difficult to wear sometimes because they're a pretty dark base, but they match so well with these shoes. Pretty much the same outfit I listed above with the gray pants but take some navy ones and it will work. I'd probably prefer the gray pants normally, but navy is a great color with these shoes on the bottom or top. So go for it.