For Restful API, can GET method use json data?
In theory, there's nothing preventing you from sending a request body in a GET request. The HTTP protocol allows it, but have no defined semantics, so it's up to you to document what exactly is going to happen when a client sends a GET payload. For instance, you have to define if parameters in a JSON body are equivalent to querystring parameters or something else entirely.
However, since there are no clearly defined semantics, you have no guarantee that implementations between your application and the client will respect it. A server or proxy might reject the whole request, or ignore the body, or anything else. The REST way to deal with broken implementations is to circumvent it in a way that's decoupled from your application, so I'd say you have two options that can be considered best practices.
The simple option is to use POST instead of GET as recommended by other answers. Since POST is not standardized by HTTP, you'll have to document how exactly that's supposed to work.
Another option, which I prefer, is to implement your application assuming the GET payload is never tampered with. Then, in case something has a broken implementation, you allow clients to override the HTTP method with the X-HTTP-Method-Override header, which is a popular convention for clients to emulate HTTP methods with POST. So, if a client has a broken implementation, it can write the GET request as a POST, sending the X-HTTP-Method-Override: GET header, and you can have a middleware that's decoupled from your application implementation and rewrites the method accordingly. This is the best option if you're a purist.
To answer your question, yes you may pass JSON in the URI as part of a GET request (provided you URL-encode). However, considering your reason for doing this is due to the length of the URI, using JSON will be self-defeating (introducing more characters than required).
I suggest you send your parameters in body of a POST request, either in regular CGI style (param1=val1¶m2=val2) or JSON (parsed by your API upon receipt)