I prepared an acrobat form that contains a drop-down list.
When I try to open the form on my smartphone, the drop-down list doesn't function.
This file should arrive to many people; how could I activate the drop-down option in the smartphone?
You can't. Instruct the users to open it using Adobe Reader for best results.
If you want a form that works reliably for everyone, without demanding they download to a computer and use Acrobat Reader, I suggest you consider HTML forms instead.