In a short clip among the DVD extras included with Charlie Chaplin’s 1928 film The Circus, a woman walks past the camera appearing to talk on a cell phone. The best explanation seems to be that she’s using a portable hearing aid, introduced by Siemens in 1924.
In 2013 the clip below appeared on YouTube, allegedly shot in 1938 and again seeming to show a woman using a cell phone. One popular explanation, that Dupont was experimenting with wireless telephones in Leominster, Massachusetts, is apparently not true, but I can’t find any plausible theories beyond that. Draw your own conclusions.