What year did Constantine move the capital to byzantium?

Constantine did not move the imperial capital form Rome to Byzantium. Rome had already ceased to be the capital when his predecessor, Diocletian, designated Nicomedia (in north-western Turkey) as the imperial capital of the eastern part of the empire and Milan (in Italy) as the imperial capital of the western part of the empire.

Constantine redeveloped Byzantium and renamed it. It became Constantinople (City of Constantine). It was inaugurated in 330.