If you meant "family" in linguistic sense, then, no. Japanese is of Japonic languages family, and Turkish is of Turkic. The proposed Altaic family (which was a

If you meant "family" in linguistic sense, then, no. Japanese is of Japonic languages family, and Turkish is of Turkic. The proposed Altaic family (which was a parent to both, in its expanded "Macro-Altaic" version) was discredited, and Japonic is generally classified as an isolate language family.