To change your ratings privacy, click your name from the right hand of the screen and select "Your Ratings" from the drop down menu. On the "Your Ratings"page, use the "Public" on/off toggle to update your privacy setting for this list.
On the IMDb mobile app, navigate to your IMDb profile by tapping in the bottom banner, tap "Account", then "Privacy settings". You may be prompted to sign-in to verify any update to these settings. From there, you will be able to select whether your Ratings are Public, Private, or Public only with reviews. Once you've selected your preferred privacy setting, tap "Save".