"rutilus", "rufus", and "puniceus" are the latin words for "red".
"caput" and "capitis" are the latin words for "head".
"saeta", "crinis", "crines", and "capillus" are the latin words for "hair".
It just depends on the context in which you are using them. I don't believe the Latin language has an actual word that embodies the idea "redhead" like the English language does, but there may be an idiom or similar that is used to refer to "redheads". but as far as I can tell: rutilus saeta (red hair) and rutilus - caput capitis (red-headed) are the proper expressions for "redhead". You could probably say "person with red hair" or "a frail-skinned beauty with a head of dancing, fiery red hair".
Rufus actually means 'Redheaded'. It was initially used like an English nickname in early Rome, but grew into becoming more the equivalent of our family name, so there were people with the cognomen Rufus with any color hair.
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Latin has several adjectives meaning red or reddish-coloured:
rubus, rubicundus, rufus, surrufus, surrubicundus, rubicundulus.
Of these, the term rufus was used as an epithet, nickname or personal name in the medieval period for someone with red hair (the son of king William I was also named William and he was given the nickname Rufus)