You are close, but not quite there. Try something like this instead:
uri = URI.parse("https://auth.api.rackspacecloud.com")
http = Net::HTTP.new(uri.host, uri.port)
http.use_ssl = true
http.verify_mode = OpenSSL::SSL::VERIFY_NONE
request = Net::HTTP::Post.new("/v1.1/auth")
request.add_field('Content-Type', 'application/json')
request.body = {'credentials' => {'username' => 'username', 'key' => 'key'}}.to_json
response = http.request(request)
This will set the Content-Type header as well as post the JSON in the body, rather than in the form data as your code had it. With the sample credentials, it still fails, but I suspect it should work with real data in there.