But 2/3'rds of the state legislators would have to pass resolutions calling for a constitutional convention.
IIRC, we are only two states' votes away from the required 2/3's. There have been a couple of state legislatures who have tried to rescind their vote, but the Constitution doesn't address rescission, so the current total stands.
All that is needed is for two more states to vote aye, and Nancy Pelosi gets to preside over rewriting the Constitution.
If you're wondering how we got in this situation, the anti-abortion movement was behind the votes. They wanted to rewrite the Constitution to abolish abortion.
Unintended Consequences of the Religious Right.