Siner was born in New York City. His father was American, born in Manhattan, New York, and his mother English, born in Bexhill-on-Sea, Sussex. His mother wanted him to be educated in the United Kingdom, and the family returned there when he was five. After attending St Edmund's School, Hindhead, he trained for the stage at the Webber Douglas Academy of Dramatic Art in London.
He is cousin to the actress Selina Cadell and her brother, the late Simon Cadell.
In 1980, Siner portrayed director Mack Sennett in The Biograph Girl, a short-lived West End musical about the silent film era. He played Lieutenant Hubert Gruber in the sitcom 'Allo 'Allo! between 1982 and 1992. Other credits include I, Claudius; Babylon 5; Seinfeld; You Rang, M'Lord?; The Brittas Empire; Leprechaun 4: In Space; Martial Law; Diagnosis: Murder; Secret Army; Star Trek: Enterprise and the Doctor Who story "Genesis of the Daleks." He also played a small role in the movie Pirates of the Caribbean: The Curse of the Black Pearl. In addition to this, he also appeared in ChuckleVision.
After 'Allo 'Allo came to the end of its run in 1992, Siner worked for a time in the United States, based in Los Angeles, California. He has since returned to the United Kingdom, and now resides in Chesham in Buckinghamshire.
Siner is one of only ten actors to appear in both the Star Trek and Doctor Who franchises.
In 2006, Siner appeared in two films by writer and director David Roden (of Dimensions in Time fame) called Beginner's Please and The Resurrectionist.
In June and July 2007, he reprised his role of Lieutenant Gruber in the stage play of 'Allo 'Allo, for Twelfth Night Theatre in Brisbane, alongside Gorden Kaye and Sue Hodge, playing their original roles of René Artois and Mimi Labonq. The other characters were portrayed by various Australian actors, including Katy Manning, Steven Tandy and Jason Gann.
Siner voiced several Star Wars video games:Star Wars: Jedi Knight II - Jedi Outcast
Star Wars: Galactic Battlegrounds
Star Wars: Force Commander
Star Wars: TIE Fighter
He worked as a script editor on two Dr Who episodesin 2008.
Siner appeared in Episode 2 of the BBC sitcom Family Tree, which first aired on British television in July 2013.