Brief disclaimer for any reader: I do not recommend using Firefox Sync with the Tor Browser. Support for this service was intentionally disabled and unless you are well aware of the privacy implications, you should definitely not re-enable it. It should also be mentioned that support for it may be completely removed in future versions of the Tor Browser and the following instructions may become obsolete.
You can sign in to the service if you disable anti-fingerprinting measures by setting privacy.resistFingerprinting to false in about:config (it can be re-enabled after).
The settings will be kept only during the current (private) session, so you may also want to disable/uncheck Always use private browsing mode in about:preferences#privacy.