I've never heard it pronounced that way, although 'care' is how the first syllable in the word 'character' is pronounced.

I've always heard it pronounced var char (the parts rhyme). Char is pronounced like when you burn/blacken a steak. "Char-grilled food is cooked over or under direct heat so that its surface becomes slightly black"

Logic dictates it should be pronounced as char-acter, but my brain brings out char-coal always.