Commercial Fixed Wing
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 456; Flight Crew Type 12000
Communication Breakdown; Confusion; Workload
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Provided Assistance; Flight Crew Became Reoriented
Human Factors; Procedure
After diverting into TUL for weather; handling passenger issues; and two maintenance issues; we departed TUL on V74 toward FSM. Reaching 10;000 feet; we were cleared direct MAYJI. A similar waypoint named MAGGE was on our route. I read back the waypoint using the same pronunciation as ATC then proceeded direct to MAGGE. About three minutes later; ATC asked if we were direct MAYJI. We then queried the Controller about the phonetic spelling. Realizing our error; we typed in the correct waypoint MAYJI and turned about 15 degrees left to make the correction.
Air carrier Captain reported a track heading deviation caused by similar sounding fix names MAYJI and MAGGE.