You can include a date in the text (see the Migrating Ancestor template's [parameter usage]), and many have, but it's not a separate parameter. So it's not something that could be pulled into a report, nor would we want to add it as a required parameter.
Years ago there was a proposal for an immigrant sticker that would have the year and add the ship category, but one was never created because of the chaos of the ship categories at the time (still a bit chaotic & not a category you'd want auto-generated by a sticker).
Perhaps a sticker whose main purpose is to inform the Ancestor Explorer app with date of immigration would satisfy both your request and that earlier one (and another one I'd had a couple of years ago). It would need to be flexible as to image, as the Migrating Ancestor template is, rather than use a ship image (as suggested by the earlier request), since not all immigrants crossed an ocean, and if they did, not all did so on a sailing ship or arrived aboard a steamer at Ellis Island.
IF (big if) the Ancestor Explorer app could be rewritten to include the year from a sticker if the sticker was used on a profile the app was collecting info from - a question for the app's creator, Chase* - then we could propose a new sticker that could be used to provide the year. I've done one up in a sandbox page - see https://www.wikitree.com/wiki/Template:Sandbox_Liz6/docs
Cheers, Liz
* From the Ancestor Explorer app page: If you have any questions, comments, suggestions or problems, please post a comment on Chase Ashley's WikiTree page.