If you've found this page you've probably been googling "can I add my Google Analytics annotations to a time series chart in Google Data Studio". As of today the answer is unfortunately still no, however here is a technique to at least add in a few key annotations to your charts to explain notable shifts in the data.
The way to do this is to create a calculated metric, name it after the event you want to annotate, and apply it as an additional metric to your chart.
To do this select create new field in the bottom right corner and use the following case statement.
What we're doing is specifying the date on which you want the annotation to appear and giving it a value of 1. We then name the field what we want our annotation to appear as.
Once you've created the metric don't hit finished, but save the metric and then return to the list of fields in your data set by click "All Fields" in the top left corner. In there you will need to find your new metric and just make sure the aggregation type is set to sum.
After you've created your metric, return to your chart configuration and add your new annotation metric to your time series.
Finally, in your chart style settings you will just need to set the series no. 2 data to display on the right axis, and display as a bar.
You can add several of these annotation metrics to your charts if required just by duplicating the above process!
One last note, if you find your annotation bars aren't spanning the total height of the chart like in my example, you may just need to set the right axis max value to 1 under the style tab.