Tequila made in the traditional way entirely from the blue agave plant is naturally gluten-free. However, some cheaper brands of tequila are considered "mixto," or not entirely from the blue agave plant, and these might contain gluten you'll need to contact the manufacturer to ask.
If the tequila bottle does not state "100% agave," then it's mixto, and contains added sugar and potentially gluten as well.
Realistically, even most cheaper tequilas will not contain gluten. But if you're particularly sensitive to gluten cross-contamination, you may want to stick to the higher quality (and unfortunately more expensive) 100% blue agave tequila those tequila varieties should be completely gluten-free.