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.