Make a new "bare" repo in dropbox
mkdir ~/Dropbox/git/new-project.git
git init --bare ~/Dropbox/git/new-project.git
cd ~/src
git clone ~/Dropbox/git/new-project.git
This creates the directory ~/src/new-project
with dropbox as the "origin" remote.
cd new-project
Rename it for clarity.
git remote rename origin dropbox
Let's make an alias to keep everything in sync.
git config alias.backup 'push dropbox --all --prune --follow-tags'
Now let's try it.
touch .gitignore
git add .gitignore
git commit -m 'INIT'
git backup