Baking Soda or Cornstarch
Both Baking soda and cornstarch are absorbent powders and have a great tendency to soak up grease and oil. Sprinkle either of the two generously over the spill and let it stay for sometime (15 to 20 minutes). Scrub the stain off using a stiff brush until you get the desired results.
You can also use a dishwasher detergent to remove fresh oil spills from concrete. Sprinkle the area generously with the detergent and allow it to stand for several minutes (five minutes or so). Then pour hot water (boiling) over the area and scrub it off with a stiff-bristled brush. Repeat the procedure until you achieve the desired results.
WD-40 a water-displacing spray that you can easily find at your nearest automotive or hardware store. Spray a healthy dose of WD-40 over the oil spill and wipe it immediately using a rag. Dispose of the rag properly. Repeat the process if you feel the stain is not completely gone.
Kitty litter also works
Kitty litter or cat litter is granulated clay which is used to absorb the waste products of pets like cats and dogs. Sprinkle kitty litter generously over the fresh spill and let it sit overnight. The litter will absorb the oil completely and you can just sweep it away in the morning. Place a heavy dose of litter onto the oil spill, otherwise you may have to repeat the procedure for a couple of times.
Treat old and tough oil stains on your concrete driveway with Trisodium phosphate. Trisodium phosphate is a widely-available all purpose cleaner. Sprinkle the chemical over the spill, making sure the area is wet. Allow it to sit for almost half an hour before scrubbing it off with a brush with stiff bristles. Rinse the area thoroughly with a water hose to finish cleaning.