Try adjusting your curl command to the following:
curl -X POST -u <deployment_user> --data-binary @"<zip_file_path>" https://<app_name>.scm.azurewebsites.net/api/zipdeploy
See this doc for more information. If you still encounter problems, please include a snippet of your deployment logs. You can access them from https://<app_name>.scm.azurewebsites.net/api/deployments.