Call asynchronous method in constructor?

The best solution is to acknowledge the asynchronous nature of the download and design for it.

In other words, decide what your application should look like while the data is downloading. Have the page constructor set up that view, and start the download. When the download completes update the page to display the data.

I have a blog post on asynchronous constructors that you may find useful. Also, some MSDN articles; one on asynchronous data-binding (if you're using MVVM) and another on asynchronous best practices (i.e., you should avoid async void).

You can also do just like this:

Task.Run(() => this.FunctionAsync()).Wait();

Note: Be careful about thread blocking!