If you are a refugee who is living in California on asylum, United States Citizenship and Immigration Services provides you with the option to become a permanent resident of the United States, as well as your spouse and any children under the age of 21. Citizenship is not a requirement and does not affect your ability to live and work in this country. However, asylum status is not permanent, and you are less likely to have any problems staying in the country if there is a change in circumstances. For example, if conditions in your home country change and you no longer have a well-founded fear of persecution due to your religion, sexual orientation or some other factor, your status as an asylee will no longer be valid.
The first step toward naturalization is to receive your green card, which you are eligible to apply for after a minimum of one year residing in the U.S. During this process, you must not abandon your status as an asylee by returning to the country from which you sought refugee status. You must also remain admissible and settled in the United States without having your asylee status terminated. You may submit green card applications for your spouse and children simultaneously.
Once you have been a resident of the U.S. for five years, you may apply for naturalization. The date of adjustment of status is moved back to one year before you received your green card, so the wait is four years from the date that initial permanent residence was granted.