Yes, and you probably should. Regular aerobic exercise is one of the few lifestyle interventions with consistent evidence for reducing tinnitus distress. It improves sleep, lowers baseline stress and anxiety, raises mood, and slightly improves cerebral blood flow — all of which feed positively into the tinnitus loop.
A few practical notes. High-intensity exercise can temporarily increase the perceived loudness of tinnitus during and just after a session, mostly through the brief rise in blood pressure and heart rate. This is normal and not a sign of damage. The loudness usually returns to baseline within an hour. If the spike bothers you, moderate intensity is fine.
Be careful in gym environments. The classes with thumping music can easily exceed 95 dB SPL, which is a noise dose your tinnitus probably does not need. Wear musician earplugs in spin and HIIT classes. Avoid lifting maximums where you hold your breath against a closed glottis; the resulting jump in middle-ear pressure can briefly worsen tinnitus.
Walking, cycling, swimming and ordinary running are all great.