Answer:
The President does not vote on a budget, but they can propose one. Congress ultimately has the authority to decide and pass a budget that the President can sign into law.
The budget process begins with the President submitting a proposed budget to Congress.
The House and Senate each then consider the proposed budget and create their own versions.
The two versions are reconciled in a conference committee and then voted on by both chambers in Congress.
If the budget is approved, it is sent to the President for signature.