Openshift is quite amazing and I strongly can say, it is much better than its competitor such as Google App Engine or Heroku in providing services.
With Openshift you not only able to do your testing and deploy your applications, but also you can host your website there very easily. For instance, Openshift it provides installer for WordPress which allows you to install it flawlessly without pushing the wordpress code manually. It is kind of automated and no need so much effort to get it done. It also provides other CMS such as Dropal and Joomola as well. See the below picture,
Furthermore, you can link your domain to your WordPress which is hosted in Openshift by changing CName of your domain to point to your Openshift account.
In order to do that, first you need to change the setting of your application, which is the change hyperlink,
After clicking on configuration you need to add your domain name under domain name field, like this picture,
Than save the changes. The configuration on Openshift side is done. Now it is time to go to your domain control panel (in this example I have used a .tk domain) and add your Openshift application URL under either URL forwarding or Cname like the following picture,
After you have done all the changes, you should be able to access to your Openshift application with your dedicated domain.