I don't know of a way to directly do this using only Git locally. If you are using a tool like Bitbucket or GitHub, then the website would show the latest commit hash in plain view.
One option to do this locally without having a lasting impact on anything would be to simply update your tracking branch. But first, record what the commit hash of the tracking branch is. So do this:
git log origin/master # record the SHA-1 hash from HEAD
git pull origin master # update the tracking branch
# find the SHA-1 hash you want
git update-ref refs/remotes/origin/master <original SHA-1 hash of origin/master>
The trick here is to reset the tracking branch to the point where it was when you started. Now you have the hash you want.
But question: What use is this hash if you don't have a tracking branch containing the corresponding commits?