So, you've done your background work already and have learned that search engines like Google prefer mobile responsive websites and may give some degree of SEO preference for websites set up that way.
You've also determined that you receive a fair amount of your website traffic from visitors on devices like smart phones and tablets, so you're keen to enhance your visitor's mobile experience.
Retrofit a Responsive Theme
The question you now have is, can you retrofit your current Drupal website with a new responsive mobile-friendly theme? The good news is that we can answer your question with a "yes", since we have added modifications to an existing Drupal theme so that the theme now displays well on smaller screen devices.
One example of how we have managed this process for a client is as a preparatory step for a whole-website upgrade. Because Drupal 8 is on its way, we have been doing this kind of enhancement for Drupal 6 websites as an interim upgrade until the time that we completely convert the website and their modules to Drupal 8.
In other circumstances, a Drupal 7 website owner who likes their existing theme can refresh the look for small screen devices and extend the life of their Drupal 7 theme.
Evaluate the Economics
However, you have to examine the economics carefully. Retrofitting an existing theme could easily approach or exceed the cost of writing a new theme from scratch. Also, if your web site is using a purchased theme, it is often better to just overlay a completely new theme than try to upgrade a purchased theme. (Perhaps the theme vendor is now offering a responsive upgrade.)