My understanding is that technically, the Senate does not ratify a treaty. They vote to give the President the OK to ratify a treaty. I am not sure what the difference is but that is the actual process.
The official language of the Constitution says the president can make treaties with the concurrence of 2/3 of the Senate. In other words without the Senate, it means nothing.
[The President] shall have power, by and with the advice and consent of the Senate, to make treaties, provided two thirds of the Senators present concur;