Maybe you could try the snap tool?
https://pro.arcgis.com/de/pro-app/latest/tool-reference/editing/snap.htm
ArcGIS has a very long and competent history of reprojecting data on the fly so data sets from different sources and projections can be used together. Unless some previous edits were made that caused the disparity in the first place I am guessing you have a projection problem going on.
Have you verified the coordinate systems of both datasets are correctly assigned? https://pro.arcgis.com/en/pro-app/latest/help/mapping/properties/coordinate-systems-and-projections....
Alternatively, if you wish to brute force the issue, you can do the move with snapping as @JohannesBierer suggested en masse. Select some number of your polygons and start the move process. The default anchor is in the middle of your selection set. Hold down Control key on anchor to relocate the anchor to a snapable location. See https://pro.arcgis.com/en/pro-app/latest/help/editing/move-or-rotate-or-scale-a-feature.htm
Respectfully,
Tom
Thanks for your reply guys but the snapping tool may work if it for small number of polys maybe where i know
how much the shift is , but in my case its thousands of polys which is hard to work
i am testing now analysis tool to convert parcels to centroid then spatial join with polys