We got the distinguished gentleman from Indiana in D.C. Thursday, and asked him if he enjoyed Hova's 4:44 tour stop at the Capital One Arena. Carson gushed about the show ... and then took his praise one HUGE step further.

Check it out ... Rep. Carson -- who grew up in a similar environment to Jay-Z -- gives a shout out to Diddy, Damon Dash and Master P ... before anointing Hova a viable candidate for the White House.

Carson for Veep?