Try 1989 for customers of Central Telephone in the United States.
That’s the date on this video from youtube and it looks to be about right.
There’s another video dated 1986 but the thing lacks any voice over or other identifying marks to suggest it is either an ad or something from about 1986.
The cell phone itself dates back way before that - try 1973 - with the first commercial product entering service in the mid to late 1970s. of course, with a handset going for about US$4,000, there weren’t a lot of them on the go.
As with home computers, consider the capabilities of cell phones back then and what they do today.
-srbp-