FeedBlitz's RSS subscriber tracking offers many ways to share posts for RSS readers, including Twitter, Pinterest, and Sharing with Facebook.
The "Like" button is enabled by default for new RSS feeds; publishers with RSS feeds created before August 16, 2010 can add the Like feature at under Social Sharing.
Under My Sites, click the RSS Feed you wish to add the Facebook Like option to.
Now click Social Sharing from the menu in the upper right.
Under Social, make sure the tick box next to Facebook Like is checked. This allows the RSS reader to "Like" the post at Facebook instead of simply sharing it. The "Like" button appears in miniature form (so it is the same height as the other buttons) along with all the other social media icons in your feed's RSS, browser and mobile-friendly versions.