How to cite a film with BibTeX

You can use biblatex!.

Here is an example, using biblatex-apa. I had to add lines stating that the director and producer should be used as authors in citations of movies.

 \documentclass{article}
    \usepackage[american]{babel}
    \usepackage{csquotes}
    \usepackage[style=apa, natbib]{biblatex}
    \DeclareLanguageMapping{american}{american-apa}
    \addbibresource{file.bib}

    \DeclareLabelname[movie]{
      \field{director}
      \field{producer}
    }


    \begin{document}
    I've seen a movie \citep{machida2015}.

    \printbibliography
    \end{document}

The file.bib file:

@movie{machida2015,
  title =   {Ex Machina},
  producer= {Macdonald, A. and Reich, A.}     
  director = {Garland, P.},
  year = {2015},
  publisher = {United Kingdom: Universal Studios.}
}