Best answer: The beta is available in India and the Philippines at the moment. It'll soon expand to Indonesia, Peru, Colombia, Egypt, and Lebanon. It's expected to roll out to more countries later this year. Pre-register now: Apex Legends Mobile on the Google Play Store
Why you can't sign up for the Apex Legend mobile beta
Electronic Arts and Respawn Entertainment first announced their intentions to release Apex Legends Mobile not long after the game launched on consoles and PC. Respawn announced in April 2021 that it'd be opening regional betas for the game this year, intending to roll the beta out to different regions throughout the year.
At the moment, the beta is only available to some players in India and the Philippines. On June 23, Respawn announced that "in a few weeks," it'd be expanding the regional mobile beta to Indonesia, Peru, Colombia, Egypt, and Lebanon.
The Apex Legends mobile beta is currently available only on Android. Respawn promises in the mobile game's FAQ that it'll be offering the game in more regions and also on iOS in the future: "As we continue with testing, we'll expand the size of these tests, add new regions, and implement iOS support. When we're ready to go broader, we'll launch a page that allows you to pre-register for the game and sign up for news about the betas."
How to know if you can join the beta
According to Respawn, the easiest way to know whether the game is available in your region is to pre-register for it on the Google Play Store. Since the beta is closed, access is currently through invitation only, slots are limited, and those invited only have a limited amount of time to join the beta.
Note that if you do get into the closed beta, the game being tested is not the complete version of Apex Legends. According to the FAQ: "To start, only the World's Edge map and some of the original Legends from the game will be playable." It's available to play on phones running Android 6.0 or higher. While it has touchscreen controls, it might be best to play it with a mobile gaming controller.