XAMARIN SPEECH RECOGNITION API

Yes, there is such functionality of Android Speech on Xamarin.

For this, you can refer to this document: Android Speech.

Before using the speech system, it is always wise to check to ensure the device has a microphone.

The code sample below demonstrates querying if a microphone is available and if not, to create an alert. If no microphone is available at this point you would either quit the activity or disable the ability to record the speech.

string rec = Android.Content.PM.PackageManager.FeatureMicrophone;
if (rec != "android.hardware.microphone")
{
    var alert = new AlertDialog.Builder(recButton.Context);
    alert.SetTitle("You don't seem to have a microphone to record with");
    alert.SetPositiveButton("OK", (sender, e) =>
    {
        return;
    });
    alert.Show();
}

For more information, please check the document above.