FORT BELVOIR, Va.—The U.S. Army has commissioned a study to determine whether an anesthetic injection to the neck alleviates symptoms of post-traumatic stress disorder—a treatment that, if proven effective, could be a big step toward easing an affliction affecting hundreds of thousands of troops who have returned from combat.

The $2 million Army study constitutes the first large-scale randomized control research into use of the shots—called stellate ganglion blocks—to treat PTSD. The injections have been used for decades for...