Is there a way to download brushes into Adobe Illustrator?
No. You can not use Photoshop brushes in Illustrator.
The application core structure is vastly different and Photoshop brushes won't work in Illustrator just as Illustrator brushes won't work in Photoshop.
Photoshop brushes are based on pixels. Illustrator brushes are based on vector paths. They simply aren't the same.
You can use a variety of different brushes within Illustrator but they must be made for Illustrator. To load a brush in Illustrator simply double-click the Illustrator brush file or choose
Open Brush Library from the menu on the Brush Panel within Illustrator.