You have not specified any information about your server-side setup.
If you are generating the json on the fly, then you should check if the request send by the browser contains Accept-Encoding: gzip
header.
If yes, then add header Content-Encoding: gzip
to the response and just sent gzip compressed data.
If the json files are static you should configure application/json
mime type as compressible in your webserver configuration, or better yet, precompress it, store both file.json and file.json.gz on your webserver and then configure conditional rewrite and headers, so the compressed file is served only to clients that supports compression.
Search/Ask ServerFault how to do this on your webserver.