Under many sane readings of the constitution, this isn’t a power congress has.
The constitution only explicitly articulates the process for establishing treaties, not ending them. So it's a bit of a gray area as to whether the president can end them by himself, since he can't establish them by himself.
To my mind, it would seem exceedingly weird if establishing a treaty required the consent of the Senate but breaking one didn't. What's the argument to be made that the two aspects (establish/break) are so fundamentally different that the rules for the first aren't also the rules for the second? Why does the president need consent to say yes but does not need consent to say no?
It's definitely been done before, but also never directly contested. (In previous cases SCOTUS has avoided answering the question by saying they didn't have jurisdiction.)