It can be bought from Ralph at Mick & Ralph's, a shop located close to Freeside's east gate. It costs 500 bottle caps, or 375 if a Barter check of 50 is passed. The passport can also be obtained as one of the King's favors at the end of the quest G.I. Blues.
A passport is not required if the Strip is entered via the monorail at Camp McCarran or with Science above 80, in which case the Securitron can be convinced to allow entrance.