In this document from 1916, on the last line of the first page is the word rôle. If context matters, the entire sentence is:
As might readily be supposed, the control of the lactic acid fermentation plays a very important rôle in the manufacturing processes of all types of cheese.
This appears to be the only occurrence of this word or character in this document.
What is the meaning of the ^ mark? Is this an old writing convention that has been lost? If so, when was it used?
It’s because the word has an circumflex in the original French and kept that as a borrowed word. As foreign words become more common in English they tend to lose accents etc because English doesn’t have them.