Yes, a sinus infection (sinusitis) or inflammation can cause a toothache — specifically in the upper rear teeth, which are close to the sinuses
In fact, pain in the upper teeth is a fairly common symptom with sinus conditions.
If you have a persistent toothache, first consult your dentist for an exam. He or she will consider possible dental causes for the toothache, such as periodontal disease, tooth grinding, cavities or dental abscesses. If your dentist rules out a dental cause for the toothache, consult your doctor. He or she will consider whether a sinus condition or other underlying medical problem is contributing to the toothache.