Short Answer
YES!
Extract of AR 670-1
Here is an extract from page 13 of AR 670-1
(d) Soldiers will not walk while engaged in activities that would interfere with the hand salute and greeting of the day or detract from a professional image. Examples include, but are not limited to, walking while eating, using electronic devices, or smoking cigarettes, cigars, or pipes. Soldiers are not authorized to wear wireless or non-wireless devices/earpieces while wearing Army uniforms. Hands-free devices while operating a personal, commercial, or military vehicle (to include a motorcycle or bicycle) are allowed if not otherwise prohibited by policy or law in accordance with AR 385–10