This is actually skirting the line of allowed use of automation from Twitter Automation Rules and Best Practices.
Automated Retweeting of Other Users
Retweeting someone means you think your followers should see their tweet. When you’re retweeting in an automated fashion, and especially based on an automated search or keyword, this becomes less true.
We discourage the automatic retweeting of other users based on a particular keyword and may suspend or terminate accounts that engage in this behavior, particularly if they are being frequently blocked and reported as spam by the users they are retweeting. If you are retweeting users just so they will see your update in their replies folder and look at your account, this is akin to @reply spam and your account may be suspended or terminated.
Now that the disclosure is complete, here is the API you'll need: Twitter Rest API Retweet.
This API call requires a valid OAuth token as well for the user executing the retweets.
The link also has an example. I'm not posting information for posterity here because Twitter changes their API somewhat frequently and even though the link will stay valid, the information within it is much more fluid.