He is most known for his role in the stage production of The Glass Menagerie. He has also appeared in Teddy Ferrara at the Donmar 2015, and Who's Afraid Of Virginia Woolf (Bath Theatre Royal). Wiley was nominated for best newcomer at the Manchester Theatre Awards in 2014. He also worked along with Fiona Hampton in The Good Neighbour (film), The Glass Menagerie (play), and the short film Run.
He has had several acting gigs in films including The Commuter (2018), Justice League (2017) and Jack Ryan: Shadow Recruit (2014), Red 2 (2013). He has also appeared on TV shows including Absentia (2017) and The Program (2015).
He is the voice narrator of ID's true-crime series Web of Lies (seasons 1,2,4-6). He has had other voice roles in video games and promos.