You sure can! If you wish to manage your incoming emails with Google Apps, you need to point your domain's MX records to Google first. Access your website's Control Panel and locate the Edit MX Record menu.
Using the Point mail to Google section you can create Google MX Records for your domain name. Just the select the Domain name you wish to use with google and click Create Google MX records.
After that, you should be able to use your email accounts with Google. To find out how to setup your email accounts to work with Gmail, take a look at this tutorial: https://www.hostinger.com/tutorials/email/how-to-set-up-gmail-for-your-own-domain