Can i get braces to close small gaps on the side of my teeth?

Yes but: A lot depends upon the occlusion (the bite or how your teeth fit together and why you have the small spaces. You may also be a candidate for bonding of acrylic to close the spaces. I would consider more than one opinion.

Possibly: If small space because just 2 teeth are out of position, limited Orthodontic treatment may help. However if you bring the 2 teeth together spaces will open on the o opposite sides of the teeth. If you have space because of a malocclusion, more extensive Ortho Rx may be warranted. If you have space because of tooth size issues, restorative Rx may be best. See Orthodontist and Dentist for info.

See an orthodontist: The most conservative and minimally invasive way to close a small gap is orthodontic treatment, either using conventional fixed braces, or invisible braces (e.g. Invisalign). Ask your orthodontist for more information.