I accidentally deleted my printer and cannot reinstall the software. it's a Cannon MG8220

That printer is a very old model, I have a similar one (MG8120). For both these printers, Canon list compatibility as "10.4 to 10.6" and what I have found is that the installer may not run on newer OS or some of the components of the Canon software may not install properly or run under newer systems.

But you can still use the printer. You can add it to your printer list, the drivers should still be on your Mac and selectable. Otherwise, you can use it with other generic drivers or the ones that come built in with the Mac OS. I am still using mine under Catalina, Mojave, High Sierra, Sierra, and El Capitan on various Macs. On some of these when scanning I have to use Image Capture, the custom software that Canon provided either won't instal;l or no longer works.

Mac OS X: About the Reset Printing System feature ...

http://support.apple.com/kb/HT1341?viewlocale=en_US

In System Preferences>Fax & Print, Right click or Control+click on the Printers list Sidebar, choose Reset Printing System.

if you hold option and click the "-" tab it resets the printing system.

http://www.macosxhints.com/article.php?story=20031215144430486

Safe Boot from the HD, (holding Shift key down at bootup).

Any devices that previously appeared in your Printer List and Fax List will need to be added again after resetting the printing system.

Resetting the printing system in Mac OS X

1. To use the Reset Printing System feature in Mac OS X, follow these steps:
2. Choose System Preferences from the Apple menu.
3. Choose Print & Fax from the View menu.
4. Control-click on list of printers on the left side of the window, then choose "Reset printing system" from the contextual menu. If you don't see a list of printers, Control-click on the text "Click + to add a printer or fax" and select "Reset printing system..."   
5. As an alternative, if you currently have one or more printers listed, you can Option-click the "-" (Remove printer) button.

http://support.apple.com/kb/ht1341

Reboot.