It's not a safety ground, so practically any gauge will do, but ...when it connects at the phonograph preamplifier's chassis I believe, which in turn should connect to the earth through the preamp's AC plug, when present.
This is another reason why the safety ground on a preamp should never b e disabled. A lethal voltage could develop at the tonearm or fire created when that wire melts due to an AC short in the preamp otherwise.
Of course, it's very very rare.
Best,
Erik