Rand has dark red hair. He is also described as essentially being "white" but with a darker tone, so tanned, which is not a fit with the pale skin and freckles associated with "ginger"
Rand was approximately 6'6" tall and weighed 235 pounds, with broad shoulders, a deep chest and a narrow waist. He had dark reddish hair, and eyes that seemed now gray, now blue; women could get quite lyrical about his eyes. He was very good-looking; many women thought him either pretty or beautiful. -The Wheel Of Time Companion.
Its important to note that the Companion is a recent publication, and depicts Rand how he looked at the end of the series.
Here is the original cover art of the hard cover.
Notice its red, almost brown, so a dark red hair.
I found this instance in The Gathering Storm (book 12)
He had reddish gold hair, maybe suggesting some Aiel blood.
This, however, was written by Brandon Sanderson and not Robert Jordan, and is the only instance ive found of lighter colored hair.
Again in book (13) Towers of Midnight it is again described as dark red.
He had deep red hair and he wore ragged clothing: