Will using cpap machine cause sinus infections?

See below. If the water reservoir is dirty or not cleaned properly it is possible. Keep it clean by replacing the water every night in addition to cleaning it at least every week, otherwise bacteria and fungi can grow in it which may cause allergic rhinitis and sinusitis. So try to keep your CPAP machine in good shape and it will help!
Rare. It would be very rare. Keep the equipment clean. If you develop symptoms of URI, consult with your sleep doctor about modifying CPAP regimen.