No, rye is not gluten-free.
Rye contains secalin, a type of gluten protein. There are three grains that cannot be eaten on a gluten-free diet: wheat, barley and rye. These three grains all contain the protein gluten, which triggers the autoimmune response seen in people with celiac disease. When readings labels, avoid foods that contain the words rye, secale (rye’s Latin name) or triticale (a wheat/rye hybrid that also contains gluten).