Это можно сделать следующей функцией:

function IsAdmin: Boolean;

var

   hAccessToken: THandle;

   ptgGroups: PTokenGroups;

   dwInfoBufferSize: DWORD;

   psidAdministrators: PSID;

   x: Integer;

   bSuccess: BOOL;

begin

   Result := False;

   bSuccess := OpenThreadToken(GetCurrentThread, TOKEN_QUERY, True, hAccessToken);

   if not bSuccess then

   begin

      if GetLastError = ERROR_NO_TOKEN then

      bSuccess := OpenProcessToken(GetCurrentProcess, TOKEN_QUERY, hAccessToken);

   end; 

   if bSuccess then 

   begin

      GetMem(ptgGroups, 1024); 

      bSuccess := GetTokenInformation(hAccessToken, TokenGroups, ptgGroups, 1024, dwInfoBufferSize);

      CloseHandle(hAccessToken);

      if bSuccess then 

      begin

         AllocateAndInitializeSid(SECURITY_NT_AUTHORITY, 2, SECURITY_BUILTIN_DOMAIN_RID, DOMAIN_ALIAS_RID_ADMINS, 0, 0, 0, 0, 0, 0, psidAdministrators);

         {$R-} 

         for x := 0 to ptgGroups.GroupCount - 1 do

         if EqualSid(psidAdministrators, ptgGroups.Groups[x].Sid) then 

         begin

            Result := True; 

            Break;

         end;

         {$R+}

         FreeSid(psidAdministrators); 

      end;

      FreeMem(ptgGroups); 

   end;

end;