Short Answer is YES. See the following extract of AR 670-1 for more information.
1–15. Wear of eyeglasses, sunglasses, and contact lenses
a. Wear of eyeglasses and sunglasses.
(1) Conservative civilian prescription eyeglasses are authorized for wear with all uniforms.
(2) Conservative prescription and nonprescription sunglasses are authorized for wear when in a garrison environment, except when in formation and while indoors. Individuals who are required by medical authority to wear sunglasses for medical reasons other than refractive error may wear them, except when health or safety considerations apply. Soldiers may not wear sunglasses in the field, unless required by the commander for safety reasons in highglare, field environments.