WPScan is a good tool to discover vulnerabilities on your WordPress website.

To install it:

sudo apt-get install git
sudo apt-get install libcurl4-openssl-dev libxml2 libxml2-dev libxslt1-dev ruby-dev build-essential
cd ~
git clone https://github.com/wpscanteam/wpscan.git
cd wpscan
sudo gem install bundler && bundle install --without test

Execute the scan on www.example.com:

ruby wpscan.rb --url www.example.com

Happy hacking!  🙂