Hello PaigeFO,
If you prefer not to use iCloud, you could sync your iPhone to your Mac using Finder: Sync content between your Mac and iPhone, iPad, or iPod touch - Apple Support. On your Mac (connected using your own account), open Finder, select your iPhone in the sidebar and click the Info tab. Check Calendar and click Apply. Note that you can also synchronize other data such as your contacts, music, photos etc..
If you want to use iCloud, it is possible to only sync calendars between your Mac and your iPhone. On your Mac (connected to your own account), connect your Apple ID: Sign in or out of your Apple ID on Mac - Apple Support. Then, still in System Settings, click your name, then iCloud and then "Show All". Check "Calendars". On your iPhone, sign in with your Apple ID: Sign in with your Apple ID - Apple Support. Then in Settings, tap your name, tap iCloud and then "Show All". Check "Calendars".