SmartTag in Google Home?

Hi all.
Can I integrate the google home in to Smartthings?
'Cause I dont find google home in the smartthings.

As far as I know, you can only link the other way, add SmartThings as a service in the Google Home app. That will allow your SmartThings devices to be controlled from the Home app and routines.

I did that, i have a smarttag and a vacuum, but the smarttag isnt there in the google home. Do you know why is that?

The SmartTags are only supported on Samsung Galaxy devices. Even other Android and iOS devices can’t do anything with them. They are also rather locked down so, for example, although the button automations are Routines you can only use the predefined one. The API is barely populated at all and the little that does appear doesn’t seem to be usable in automations. So if SmartThings itself can barely use them, Google has no chance.