Yes, RSA Authenticator app for iOS and Android works in China. However, please consider the following information depending on your operating system, and your device brand.

General

RSA has obtained the required local ICP Certification (渝ICP备2021001788号-4A ) for its app to published and available on App Stores in China.  This ICP certification value can also be found in the app, under "More.../About"

iOS

The Apple App Store is generally available in China.

No known issues are associated with using RSA Authenticator app for iOS in China.

Android

Google Play Store is not available in China.

All Google Play Services, are currently unavailable within China. This means that Android devices in China cannot receive Authentication pushed notifications from RSA to their devices. Users must swipe down in the RSA Authenticator app main screen to retrieve these notifications.

RSA got the required China SCC Certification to publish its app on Local Android App Stores, and is working to to make it available on:

• Huawei App Store
  • RSA Authenticator app is now available only in the 'China' Region of Huawei App Store.  Please make sure user select the correct region when accessing the Huawei App Store.
  • Direct web link to access the app is: https://appgallery.huawei.com/app/C112393703 
  • Please note that the RSA Authenticator only works with Harmony OS.. It doesn't work with Harmony OS Next, which no longer allows running Android applications.
• Honor App Store
  • RSA Authenticator app is now available on the Honor App Store.
  • There's no web interface for this app store, direct link to access the app from a mobile device connected to Honor app store is: honorstore://details?id=104488618
• Xiaomi App Store
  • Publication of the RSA Authenticator app store on Xiaomi App Store is currently under review.

For any other Android devices in China, users may be able to access Huawei/Honor/Xiaomi app stores

• Download/install the relevant app store application from Huawei / Honor / Xiaomi
• Modify device setting to allow app installation from other app stores (Settings → Security → Install unknown apps)

Please note that while these app stores support generally installation on other brand devices, they may not supported all other brand devices, and they do not seem to publish a list of supported/unsupported other brand devices.

For Android devices still not able to access one of the app stores mentioned above, RSA made the Android binary available from the RSA community.