Yes, under the Commerce Clause power.
"It does not have the power to regulate that which may affect commerce."
Not true. Under the Necessary and Proper Clause (Article I, Section 8, Clause 18) of the U.S. Consttution, Congress has the power "to make all laws which shall be necessary and proper for carrying into execution the foregoing powers".
Pualey, Congress has the power "To regulate Commerce with foreign Nations, and among the several States". It does not have the power to regulate that which may affect commerce. Sorry.