AR 600-20 is very clear on this issue. It is a NOGO. Here is an extract of AR 600-20. I would strongly encourage you to read the entire paragraph as it pertain to Fraternization.
EXTRACT OF AR 600-20
4–14. Relationships between Soldiers of different rank a. The term “officer,” as used in this paragraph, includes both commissioned and WOs unless otherwise stated. Theprovisions of this paragraph apply to both relationships between Army personnel (to include dual-status military technicians in the Army Reserve and the ARNG) and between Army personnel and personnel of other militaryServices. This policy is effective immediately, except where noted below, and applies to different-gender relationships and same-gender relationships.b. Relationships between Soldiers of different rank are prohibited if they