TensorFlow.js runs anywhere JavaScript can run so yes that includes mobile devices via the mobile browser too.
On Android getUserMedia is very well supported - you can access front or rear facing cameras with out issue. On iOS you will  need to use mobile safari possibly as iOS ecosystem is very closed, but it does work! You can check websites like can i use for support: getUserMedia/Stream API | Can I use... Support tables for HTML5, CSS3, etc 1
If you are using in native application then I believe you would need to use react native implementation of TFJS to do so:

  
      

      blog.tensorflow.org
  

  
    

TensorFlow.js for React Native is here!

  The TensorFlow blog contains regular news from the TensorFlow team and the community, with articles on Python, TensorFlow.js, TF Lite, TFX, and more.


  

  
    
    
  

  


Like this guy did:

  
      

      Medium – 20 Jul 21
  

  
    

How to use tensorflow.js in react.js — Sentimental Analysis

  In March 2018, Google announced Tensorflow.js version 1.0, which enable developer to use machine learning (ML) models directly in browser…

  
    Reading time: 5 min read