Can I put an image of the internet in an ImageButton?

I think the simplest way is this:

URL imageUrl = new URL("url_da_imagem"); 
Bitmap imagem = BitmapFactory.decodeStream(imageUrl.openConnection().getInputStream());
meuImageButton.setImageBitmap(imagem); 

Source SOen

However, the correct thing is to do this in an AsyncTask :

private class DownloadImageTask extends AsyncTask<String, Void, Bitmap> {
    ImageButton imageButton;

    public DownloadImageTask(ImageButton imageButton) {
        this.imageButton = imageButton;
    }

    protected Bitmap doInBackground(String... urls) {
        URL imageUrl = null;
        try {
            imageUrl = new URL(urls[0]);
        } catch (MalformedURLException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }
        Bitmap imagem = null;
        try {
            imagem = BitmapFactory.decodeStream(imageUrl.openConnection().getInputStream());
        } catch (IOException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }
        return imagem;
    }

    protected void onPostExecute(Bitmap result) {
        imageButton.setImageBitmap(result);
    }    
}

To put the image in your ImageButton do:

ImageButton imageButton = (ImageButton) findViewById(R.id.doSeuImageButton);
new DownloadImageTask(imageButton).execute("url_da_imagem");  

You must add the following permission to AndroidManifest.xml

<uses-permission android:name="android.permission.INTERNET" />

First you need to download this image because there is no direct way to inform a URL directly in the src property, for example.

You can have a method like this to download and get a Drawable :

public Drawable drawableFromUrl(String url) throws IOException {
    Bitmap x;

    HttpURLConnection connection = (HttpURLConnection) new URL(url).openConnection();
    connection.connect();
    InputStream input = connection.getInputStream();

    x = BitmapFactory.decodeStream(input);

    return new BitmapDrawable(x);
}

And then, just set the property of ImageButton :

btn.setImageResource(drawableFromUrl("http://..."));

I have not tested, but you will probably have to do this in a thread other than UI .