No, the placement of the ® symbol does not adhere to any specific rules. For example, the USPTO advises putting it "anywhere around the trademark". Most brand owners choose either upper-right or lower-right corner placement.
The only regulation you have to keep in mind is that in most countries, you are only permitted to use the symbol after your trademark has been registered with the corresponding intellectual property office and not sooner. You can use the ™ mark instead before your application gets approved.
Also, you can only use the ® symbol with the exact version of the mark that was registered, i.e. if you have multiple versions of your logo but only registered one as a trademark, you can only use the ® symbol with that version.