Do I have to use Link monsters on my Yu-Gi-Oh! Deck?
Using Link Monsters is optional.

It's the same case if you decided to, say, build a deck without any Trap cards.

If your deck or strategy doesn't require them, you can play without having to have one.

However, if you plan to play in tournaments, or play competitively, I'd suggest you include or at least considering using Link Monsters, as your options could improve (and because the meta game is tending towards using Links).