Crawford moved to the United States in the early 1980s, finishing runner-up twice in the Can-Am series. He finished fourth on his CART debut at Long Beach in 1984 and went on to become a regular in the Indianapolis 500. It was there in 1987 that Crawford suffered a crash in practice which resulted in serious leg injuries. However, he recovered sufficiently to return to the 500 in 1988, leading the race for a few laps. A late race puncture dropped him from 2nd to 6th.