Yes you can. (In fact, some folks think there are too many crooks working in government, but that's another story). Uncle Sam has no general prohibition against hiring ex-offenders. Each individual's history is taken into account during the hiring process. However, there are a few specific jobs, such as those involving firearms, where some types of criminal history will disqualify you for the job.
Need more information? Newspaper archives are one of the best online research tools.