When you add your data to ArcMap, perhaps as an XY event layer, you need to associate/define its current coordinate reference system.
I'm very familiar with this area of ArcGIS (I work at Esri), and so I grabbed an existing prj file that uses WGS84 and polyconic, updated the name and the projection parameters, and it should be ready to go. The well-known text string is:
The string has been reformatted into multiple lines for display.
Create a new text/ASCII file (using Notepad) and copy/paste the string into it. Remove the line breaks so you the string is in a single line. Save it. When you add the XY Event layer, use the import option to browse to this file and use it for the data's coordinate system.
I did not bother to modify the existing geographic coordinate reference system, WGS84. The difference between using the WGS84 ellipsoid and the GRS80 ellipsoid when the GeoCRS/datum is WGS84 is minor (like sub-cm).