CHICAGO—The U.S. Army is experimenting with new recruiting tactics as it struggles to connect with young people who have other job options in a strong economy.

Last year the nation’s largest military branch recruited just under 70,000 troops, about 10% short of its target of 76,500, which marked the first time in a decade the Army missed its goal. For this fiscal year ending in September, they met a more-modest goal of 68,000.

Experts...