As already noted by gezzed in his comment, meanwhile there is a good solution (described in Polling must die: triggering Jenkins builds from a Git hook):
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Set the Jenkins job’s build trigger to Poll SCM, but do not specify a schedule.
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Create a GitHub post-receive trigger to notify the URL
http://yourserver/jenkins/git/notifyCommit?url=<URL of the Git repository>?token=<get token from git to build remotely>
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This will trigger all builds that poll the specified Git repository.
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However, polling actually checks whether anything has been pushed to the used branch.
It works perfectly.