You'll have to wait three to five years in most states. A DUI will be wiped in some locations after three years, just like any other traffic violation. It will be on your driving record for 10 years in California.
It's important to remember that a driving record is not the same as a criminal record. A DUI conviction might have a long-term impact on your life.
The information in this answer is general in nature and is not legal or insurance advice for your specific situation. Policy language varies carrier by carrier; your declarations page is the final word. If you're unsure, call your agent before you need to file.