Create the site column as a separate action from the content type, and then use a "FieldLinkCreationInformation" object to add the site column to the content type. See this page on msdn for a code sample, or google "FieldlinkCreationInformation" for more examples. Or, following is an incomplete PowerShell snippet with the important bits:
#load the existing site columns $context.Load($web.Fields) $context.ExecuteQuery() #get a reference to the site column that needs to be added to a content type $mySiteColumn= $web.Fields.GetByTitle($siteColumnName) $context.Load($mySiteColumn) $context.ExecuteQuery() #Get the FieldLink, and add it to the content type $mySiteColumnLinkInfo = new-object Microsoft.SharePoint.Client.FieldLinkCreationInformation $mySiteColumnLinkInfo.Field=$mySiteColumn $varthrowaway = $myContentType.FieldLinks.Add($mySiteColumnLinkInfo) $myContentType.Update($true) $context.ExecuteQuery()