It's possible to do in principle at least, assuming all your users have modern browsers. You could use the Javascript file API to intercept file uploads and then to encrypt the data before it is sent to the server. You could then use XHRs to collect the encrypted binary data and decrypt it before presenting it to the user. If it was an image, you could use canvas to display the decrypted content.

You'd have to contend with what is probably a large performance hit, and I don't know of any libraries that do this so you'd need to spend a considerable amount of time writing one. I suspect that this approach would only be practical for very simple web applications. For instance, an encrypted image or file hosting web application might be a possibility.