Is it possible to call an async function inside a constructor in react-native?

You can't do it inside constructor, because constructor can't wait for await
So you can have another function(for example b()) for all the processes you want to run after async a(). And you have two choice for doing this:

1- use async/await:

async componentDidMount() {  
    try {
      await a();  // it will wait here untill function a finishes
    } catch(err) {}

    b(); // after function a finished, this function will calls
}

2- using .finally:

componentDidMount() {
    // in below line, function `a` will call, and when it finishes, the function inside `.finally` will be notified
    a().finally(() => {
        b(); // now your function `a` finished and you can call extra process in function `b`
    });
}

Asynchronous constructor is a potential antipattern because it doesn't result in behaviour that is expected from it.

Asynchronous side effects are supposed to happen after a component is mounted and thus occur in componentDidMount, this is what it's for. It's impossible to delay the lifecycle of a component and it's incorrect to think about it in these terms.

It's supposed to work like:

class Foo extends Component
  async a() {...}

  async componentDidMount() {
    await this.a();
  }

  render() {
    (conditionThatIsTrueWhenThereResult) ? (
      <div>...the result from a...</div>
    ) : (
      <div>fallback</div>
    );
  }
}

If it's necessary to keep a component synchronous, a asynchronous side effect should be moved to parent component that renders a child only when the result from a is ready to use.

Call a() in componentDidMount like so:

async componentDidMount() {
       await a();
       otherFuncions()
}

otherFunctions() will only be executed after a() is completed