Legal Question in Criminal Law in California

'Conviction' of a felony bars you, not a misdemeanor.

Also:

many felony and misdemeanor convictions [not infractions] can sometimes be 'expunged' by proper application and Petition to the court, but only if there was no prison time served or even sentenced, if it was not for certain sex and Domestic Violence crimes, if all terms of sentencing and probation [and at least one year of probation] are completed and finished, and if there are no new charges pending. If successful, the conviction would be retroactively withdrawn and the charges dismissed. That does not 'remove' the conviction, but merely changes the record to show 'conviction reversed and dismissed by expungement'. If expunged, you would be able to say 'no' to conviction on most private employment applications. However, the conviction is still a 'prior' for purposes of repeat offense, and must be disclosed on any application for government and professional licensing, bonding, security clearance, etc. The agency and employer then can decide whether you are barred from employment because of your conviction. If you�re serious about doing so, and you think you qualify, feel free to contact me for the legal help you'll need.

There are other prohibitions on firearm ownership in California, other than conviction for a felony. Petty theft (as governed by Penal Code sections 488, and 490) is a misdemeanor, and does not appear on the list of charges in Penal Code section 12021 subdivision (c)(1). If you were charged and convicted of one of those charges, you would be prohibited form owning a firearrm for a period of 10 years from your conviction.

You also would not be allowed to have a firearm if restriction from firearm ownership was a specific term of your probation.