I’ve hear it before, but can’t seem to find an actually source that says it is a common phrase used. As far as I know, it means to kick someone out. But let me know if you’ve used it before or if it is correct to use such expression.
to run someone out OED
P5. orig. U.S. to ride (also run) a person (out) on a rail: to carry or parade a person astride a rail as a punishment (now hist.); (fig.) to punish or drive away with ridicule.
Yes, it is correct AmE, as in:
1935 J. T. Farrell Judgment Day
They ought to be jailed, run out of town on a rail, tarred and feathered.
1975 J. Gores Hammett
They just about ran him out of St. Mary's County, Maryland, on a rail.
They're probably not fresh faces at all—perhaps they've just been ridden out of Adelaide on a rail.