So, you want your git repo to look like this:
<projectdir>
/.git
/webroot
/assets
To do this, you must move the existing files in your repo into a new webroot
subdirectory.
cd <git repo root>
mkdir webroot
git mv <all your files> webroot
git commit --all -m "moved all existing files to new 'webroot' directory"
Then, on your local filesystem you want to relocate your clone one directory above where it is now:
cd <projectdir>
mv webroot/* .
rmdir webroot
Then you want to add the assets
directory (and files) to the git repo:
git add assets
git commit -m "added assets to the repo"