Like many U.S. colleges, Wichita State University wants more foreign students but isn’t a brand name abroad.

So the school, whose mascot is a muscle-bound wheat bundle, in late 2013 started paying agents to recruit in places like China and India. The independent agents assemble candidates’ documents and urge them to apply to the Kansas school, which pays the agents $1,000 to $1,600 per enrolled student.

Overseas...