Is there any reputation limit/range a user must have to become a moderator?...
Documented on the blog
You mean a diamond moderator? (A person with a diamond next to their name)
No. But elections for moderators are held to decide who gets to be one. Sometimes in those elections, there are requirements. The last election required 7,000 reputation. It could be more in the future.
If you look at how the powers are set up, by 10,000 reputation, you will have a lot of the powers already given to moderators. This is very much intentional because overall, the community moderates more than the moderators.
While you might not have the ability to close a post with a single vote, or merge tags, those powers are generally not necessary on a day-to-day basis. Those powers are entrusted to people who the community trusts to rule over them.