に is used there because the target of 廻って来る has a sense of direction, just like ～に行く, 渡る, 届く or 向かう. Even when only は or も is used after target, に is just disappeared behind it (e.g. 学校（に）は行く, 向こう側（に）も渡る).
Sometimes it is a bit much to explicitly translate or think of も as "also". The nuance is that a lot of other people out there were already lucky and finally it's come around to the speaker, too.
Dropping the に wouldn't be outright ungrammatical but like Toritoribe-san says, it's more intuitive to have it because 回る carries a sense of movement.