Only state legislatures can do that. Congress has no say as to who may appear on state ballots. That is entirely a state issue.
People need to understand that November 4th isn't a federal election. It's 50 state elections (plus the District of Columbia). And when we cast our votes, we're not electing a president, we're appointing our respective state's electors.
And Article II of our Constitution leaves the appointing of electors entirely up to the states.
Granted, it is 50 state elections. But it is a joint session of the U.S. Congress that certifies the election. Therefore ultimately they have the responsibility to certify that the candidate is valid.
Certainly, the congress can pass a law to have the executive branch verify the eligibility of everyone appearing on any state ballot for president.