You are on the right track, but using backticks instead of pipe.
du -k `git ls-files` | awk '{total += $1} END {print total}'
If you need to worry about spaces, then git ls-filesthey xargscan and do speak in zeros:
git ls-files -z | xargs -0 du -k | awk '{total += $1} END {print total}'
, git ls-files | -, du -k | . , !