Convert SQLite ROWID to primary key

I have a large table without a primary key. Instead, I've been using the built-in ROWID as one.

Problem: now I can't VACUUM my database, because:

The VACUUM command may change the ROWIDs of entries in any tables that do not have an explicit INTEGER PRIMARY KEY.

How can I convert the ROWID to an INTEGER PRIMARY KEY, preserving existing ROWIDs and their behavior (or otherwise get VACUUM to not mess up ROWIDs)?