You may use cURL or Postman REST Client to perform a PUT request.
Send cURL command as follows:
curl -v -u username:password -X PUT -H "Content-Type: application/json" --data @"/Users/admin/work/atlassian-support/workshops/epiclink.json" http://localhost:6310/j6310/rest/api/2/issue/10141
Example of JSON data
Using Postman REST client
The returned response will show 204 No Content error although the Epic Link is successfully updated. This is a bug -
JRA-43437Getting issue details...