Yes, you can! Generally you have to buy 1-10 shares to become eligible for a Company's DRIP plan. However, some companys have what I call Fake DRIP's which charge you each time your money is reinvested But from a site called
http://www.moneypaper.com , click on "Review investor-friendly plans" for a list of DRIP companies that reinvest every penny of your dividends.
Moneypaper changes a one-time small administrative fee of $30-$50 for setting up your account. It's well well worth it. I tried to set up a DRIP myself once and don't think I own that share yet.