Can someone who has been convicted of a felony serve on jury duty in CA?

Unless there has been a recent, highly unlikely, change in the law, 'No' ex-felons can not serve on a jury in CA.

It is possible for someone who has been convicted of a felony to serve on jury duty in California if the person petitions the court for relief under Penal Code section 1203.4 and the petition is granted. Penal Code section 1203.4 allows a defendant to withdraw his or her plea of guilty or no contest (or set aside a guilty verdict after a trial) and the complaint is thereafter dismissed. If the petition is granted, the defendant must be released from all penalties and disabilities resulting from the conviction. There are several limitations to this rule, however, jury service does not appear to be one of them. Not everyone is eligible for 1203.4 relief, however. If you had to serve any time in prison as a result of your conviction you are not eligible for 1203.4 relief.

Under most circumstances no.