Is there an easy way to move an existing question I wrote from Stack Overflow to Server Fault without reposting the question on Server Fault?
Flag the question for "moderator attention" and state your request.
If you have enough reputation you can cast a close vote as "off-topic," but that needs 5 votes to get it closed and it is not guaranteed to be migrated to the other site.
You need to flag the question to allow a moderator to migrate the question.
Note that the guidelines for what questions are migrated are rather strict. It's important that the question not only follow all of the rules for a question on the target site, but that it be a good question the target site would really want. Effort is made to not migrate questions that will just be closed or need further editing.
Even moderators can't migrate questions that are more than 60 days old.