Can users rotate or move an entire polygon in Collector for ArcGIS?

Answer

Note:
The functionalities of ArcGIS Collector, ArcGIS Explorer, and ArcGIS Tracker are now available in ArcGIS Field Maps. There are no new capabilities planned for these apps—all future updates will be focused on Field Maps. Migration is recommended. See ArcGIS Blog: Migrate to Field Maps for more information.

No. The option to rotate or move an entire polygon in Collector for ArcGIS while keeping a fixed shape is currently not available.

However, users can edit the polygon and move each individual vertex by dragging them to a new location, specifying an exact x-y location, or moving the polygon to a location relative to its current position.