I’m not sure what you mean by “action film,” but film adaptations of the Bram Stoker novel, Dracula, go back to at least 1921, and possibly further.
There is an argument about this among film aficionados. There has been a rumor for at least nine decades that there was a 1920 film made in the Soviet Union based on Stoker’s book by the name of Дракула (Drakula). This film would have predated the lost 1921 Hungarian film, Dracula’s Death, and is thus claimed by many to be the first adaptation of Dracula.
The oldest existing film is the 1922 silent, Nosferatu: _eine Symphonie des Grauens_ (“Nosferatu: A Symphony of Horror”), which caused Stoker’s estate to sue for copyright infringement. Made by film director F. W. Murnau, the horror film took the story of Dracula and set it in Transylvania and Germany. In the story, Dracula’s role was changed to that of Count Orlok, played by Max Schreck.
The Stoker estate took exception to these changes, won its lawsuit, and all existing prints of Nosferatu were ordered destroyed. However, a number of pirated copies of the movie survived to the present era, where they entered the public domain. Copies of Nosferatu can now be found for download on many sites including the Internet Archive and YouTube.