Is your Excel Data of points that make up the polygons? Also, is there an ID field that identifies which points are part of which polygons? If so, the workflow would be check the Excel data to make sure it is "GIS compatible", import the Excel data to GIS, save the resulting import as a point shapefile (or feature class in a geodatabase), then build the polygons from points.
Before importing to ArcGIS, be sure the Excel spreadsheet has been "cleaned up" to GIS standards. This will help avoid issues after import.
Formatting a table in Microsoft Excel for use in ArcGIS—Help | ArcGIS for Desktop
Adding the Excel table to ArcGIS
Adding a Microsoft Excel table to ArcMap—Help | ArcGIS for Desktop
Once the Excel data is in ArcGIS, be sure to save it out as its own shapefile, as the initial display is an "Event layer" and is just temporary.
To convert the points to polygons, there are several methods. Note that some depend on what license level one has and one method involves a third-party add on (ET Geowizards). For the latter, I believe one can download a demo copy for free.
Also, some of the methods rely in part on using a File or Personal Geodatabase during the processing. If so, from the beginning import save to a geodatabase, do the processing, then export the final product once the polygons are completed to a shapefile.
How To: Convert a point feature class to a polygon feature class
Chris Donohue, GISP