This is what worked for me in a Rails 4:

# JSON data as first argument, then parameters
patch :update, { some: 'data' }.to_json, id: id, format: :json

Rails Long Term Support

Rails LTS provides security patches for old versions of Ruby on Rails (2.3, 3.2, 4.2 and 5.2)

Sending raw JSON data to a member action in a controller spec