Unfortunately, no. No web browsers have implemented any bridges between beacon detection and JavaScript.
I don't think a plugin approach is possible on mobile browsers (either iOS or Android), because neither browser supports asynchronous communication between external apps and JavaScript in Mobile Safari / Mobile Chrome. The best you could do is have a custom app that responds to a beacon, then launches a web page in the browser. But I realize that isn't what you are asking for.
If you want to build a native app with JavaScript, you can use Cordova (aka PhoneGap) and use plugins that provide beacon support. My company has one for our ProximityKit beacon framework:
https://github.com/RadiusNetworks/proximitykit-plugin-cordova
There is also a Cordova plugin that has basic beacon support here:
https://github.com/petermetz/cordova-plugin-ibeacon