WASHINGTON—Few law enforcement jobs are more coveted than the FBI’s special agent positions, but the tightest labor market in decades is forcing the bureau to do something it has rarely had to do: aggressively recruit candidates.

A slump in the number of special agent applicants—from a peak of 68,500 in 2009 to 11,500 in the year that ended in September—has forced the nation’s top law enforcement agency to overhaul its recruitment, increase its outreach, target women and minorities and relax some eligibility requirements,...