WASHINGTON—The White House has authorized U.S. troops and advisers to deploy in Central Africa to help track down the leaders of the Lord's Resistance Army rebel force—expanding the Obama administration's string of interventions around the world, and stepping into the center of a conflict that has alarmed human-rights groups for more than a decade.

The armed contingent has already begun arriving in a region where the U.S. faces a growing list of security concerns—including Al Qaeda offshoots in Somalia and Yemen, extremists...