Yes, this process is called "geocoding." The Google Maps API provides two methods for performing geocoding. If you wish to geocode from within your Google Maps API application you can do so using the GClientGeocoder object. Alternatively you can send geocoding requests directly to the HTTP geocoder.
For more information on geocoding, please see the documentation. Also please be aware of the usage limits that apply to geocoder requests.
Please note that use of the geocoder for any purpose other than obtaining locations that will be displayed using the Google Maps API is a violation of the Terms of Use. You may use the HTTP geocoder to geocode addresses outside of your Maps API application so that they may be cached and later displayed using the Google Maps API, but locations obtained using the HTTP geocoder may not be used by any other application, distributed by other means, or resold.