An Etymological Dictionary of the German Language/Annotated/Renntier
Renntier, neuter, ‘reindeer,’ Modern High German only, from the equivalent Swedish ren, which is derived from Old Icelandic hreinn (Anglo-Saxon hrân), whence also Dutch rendier, English reindeer; from the same source probably are Italian rangifero, French rangier (and renne), ‘reindeer.’ Old Icelandic hreinn is usually considered to be a Finnish and Lappish loan-word (raingo).