Your command line should have a -d/--data inserted before the string you want to send in the PUT, and you want to set the Content-Type and not Accept.
curl -H 'Content-Type: application/json' -X PUT -d '[JSON]' \
http://example.com/service
Using the exact JSON data from the question, the full command line would become:
curl -H 'Content-Type: application/json' -X PUT \
-d '{"tags":["tag1","tag2"],
"question":"Which band?",
"answers":[{"id":"a0","answer":"Answer1"},
{"id":"a1","answer":"answer2"}]}' \
http://example.com/service
Note: JSON data wrapped only for readability, not valid for curl
request.