For what it’s worth, gzip is only really effective on large objects. If your JSON responses are, like most, smaller than 1 KB or so, gzipping them won’t reduce their size appreciably.
That being said, you can enable compression for application/json data by adding the following to your domain’s .htaccess file. (For a domain using Passenger, this goes in the /public directory.)
AddOutputFilterByType DEFLATE application/json