Marc Anthony to Shannon De Lima -- This Tattoo's for YOU ... and America

Marc Anthony is making things permanent with his new 24-year-old hottie -- by branding himself with a tattoo of the Statue of Liberty ... a tribute to his GF and his new found "freedom."

Sources close to the singer tell TMZ ... Venezuelan model Shannon De Lima was with Marc when a spot-on replica of Lady Liberty was tatted inside his right wrist on New Year's Eve in Miami. Marc's 17-year-old daughter Ariana (above, right) was also front and center.

We're told "Statue of Liberty" is Marc's pet name for Shannon ... because she "freed" him from his past. While he was at it -- Marc and Ariana also got unspecified matching tats on their outer wrists.