Yes, you can apply.
The application will instruct you to identify each and every criminal conviction you have, and you MUST do this or you will be denied the license for the failure to disclose. The application will also ask you to state the facts and circumstances on which the conviction was based. Make sure that your statement is complete, that it does not discount the severity of the act, and that in it you take responsibility for the act and for the bad judgment of committing it.
Assuming that you make the required full disclosure, the Dept of Insurance will consider a number of factors in deciding whether the conviction is cause to deny or restrict an insurance producer's license. Critical considerations are the nature of the act, the length of time since the conviction, satisfactory completion of all probationary terms and conditions, other criminal acts in your history, evidence of mitigation and evidence of rehabilitation. Many of these factors are spelled out by California statute. The Dept will then send you notice of its proposed decision.
Expect, at best, an initial offer by the Department to issue you a restricted license.
You have the right to challenge the Department's decision by taking the matter to a fair hearing before an administrative law judge.
It is sound practice to consult an experienced licensing attorney BEFORE filing your license application. For very little time (and therefore relatively little fees), an attorney can assist you in crafting the required disclosure statements which may have a significant impact on the Department's initial decision. By all means, obtain skilled licensing legal counsel if the initial decision is unfavorable. A licensing lawyer can tell you whether you have a good case to challenge the initial decision and, if so, can present your best case at the hearing.
You have provided no facts about your previous conviction, so I cannot offer any application of the information provided here to your specific facts. But, in general, the older the conviction, the better your case in favor of issuance of the license.
License Advocates Law Group LLP