It depends on the warrant. The issuing magistrate will indicate on the warrant if the warrant can be cited out or if bail will need to be posted.
A cite release on a warrant allows the officer to issue the suspect a citation with a new appearance date, which will clear the warrant from the system. If the magistrate required bail on the warrant, the suspect will have to post bail in order to be released.
If you are taken into custody and booked, your warrant is automatically cleared. Note, warrants are issued by the Court and not Atascadero Police Department. They may be re-issued by the Court without notice or warning for a variety of reasons; the most common being "failure to appear".