Yes, caret is a word. It is the name for this symbol: “^”. It is used in the publishing industry to indicate where an insertion needs to be made. It is sometimes written in subscript: “^”.
Although it is pronounced the same, its meaning is not related to carat or karat, which are terms used to measure gold and gemstones.
You can use the QuillBot Grammar Checker to ensure you use words like caret correctly.