You can build the docs with:

cd doc/
make html

then modify .gitignore and add the _build folder temporarily so you can deploy the new docs:

cd ..
sed -i "" '/doc\/_build\//d' ./.gitignore
git add .gitignore
git add doc/_build/
git commit -m "Edit .gitignore and add new docs to deploy them"

make a subtree and push it to gh-pages with:

git subtree split --prefix doc/_build/html -b gh-pages
git push -f origin gh-pages:gh-pages
git branch -D gh-pages

finally, reset the last commit and checkout .gitignore:

git reset HEAD~
git checkout -- .gitignore