To create a private circle on the web:
Click the settings icon on the top-right corner of the left panel.
Click the New Circle tab.
Enable Make private button.
Then, click Save.
Note: To make private your existing circle: Go to Settings > Circles > Click the circle > Edit the details > Save.
To create a private circle on mobile:
Click the Circles icon in the lower-left corner.
Click the Pencil icon in the upper-right corner.
Click Start a new circle.
Enable the Set as private button.
Then, click Create.
Note: To make private your existing circle: Click the Circles icon > Tap the circle that you want to set as private > Click the 3 dots on the upper-right corner > Click Edit circle > Enable the set as private button > Click update.