Besides real-life cultures, the videogame Tyranny uses rings as currency:
These rings aren't really coins, but more like loops of metal. They also aren't worn on fingers, but on strings, ropes, or leather cords tied around the waist or neck. In fact, as stated in the linked wiki article:
"As rings are used as currency, it is considered vulgar to wear rings as adornment or jewelry. Such decorations are seen as vulgar, and those who wear them are held in contempt."
Of course, you're free to invent whatever customs you like.
Threading rings with cords or tying them with ropes makes for easier transport (and would allow individuals to carry more than 18 rings (assuming 2 per finger and 1 per thumb) at a time.
If what you're looking for is more like coins with holes, you might still tie them together with cord or string, for ease of use. Specific stacks of rings might be a standard lump sum. For example, a string holding 10 copper rings might be the in-universe equivalent of a €5,- bill.
That might lead to slang terms for specific amounts of money. Think of people referring to 1 dollar as a 'buck' in reference to deers, which were hunted so much that a deer hide at one point only cost 1 dollar. Hence, a buck. Or I've heard people refer to 100 dollar bills as Franklins, in reference to the guy depicted on the bill.
Of course, you can always carry rings in a purse or bag instead. That might be less vulnerable to theft, depending on the construction of the bag and cords under consideration.