expression, godan verb (-ru)
count on one's fingers
Literally 'to bend one's fingers'; used for counting by folding fingers one by one.
彼は指を折って日数を数えた。
He counted the days on his fingers.
指折り is a noun meaning 'leading' or 'prominent', often used as 指折りの (e.g., 指折りの専門家). It does not mean the action of counting on fingers.
Compound of 指 (finger) + を (object marker) + 折る (to bend). The expression is transparent and literal.