You can not delete the commit history from a branch, but you can create a new branch (without history because is new), push the files to the new branch and then delete the old branch.
The next example shows how to recreate the master branch.
# Create temporary branch
$ git checkout --orphan temp
# Add and commit all the files
$ git add -A
$ git commit -m "init"
# Delete current branch
$ git branch -D master
# Rename current branch to master
$ git branch -m master
# Push all the files to the new master branch
$ git push -f origin master