You have the right to file an appeal with the Appeals Council. Any appeal should be filed immediately following the denial by the Administrative Law Judge as you only have 60 days from the date on the decision to file your appeal.
In the alternative, you have the right to reapply and start a new Social Security claim. Unfortunately, you can no longer file an appeal and file a new application at the same time anymore.
Click here for more information about the Appeals Council level of appeal.