It turns out there is but it's not enumerated in the first amendment, so it's called an "implied right." It's been derived by the courts (including the Supreme Court) as logically inferred by the rights which are enumerated in the 1st amendment. What I found interesting is the boundaries of this implied right to silence are currently less well-defined than than the other 1st and 5th amendment rights. Apparently, some cases the court will be deciding this year may involve further fleshing out these fuzzy edges. I'm not an expert but as I recall, the scenarios may include things like whether social media networks can be compelled by a legislative statute to disclose (ie 'speak') their content moderation policies and whether public universities can enforce codes of conduct which may compel speech.
Personally, I'm all-in on the vital necessity of robustly expansive free speech rights, so I'm also all-in on robust freedom of silence rights. I used to think I understood the limits of free speech in the U.S. but reading this article by 1st amendment expert Ken White on free speech tropes surprised me. Highly recommended: https://www.theatlantic.com/ideas/archive/2019/08/free-speec...