When Madara was near death he gave the Rinnegan to Nagato, and Nagato's eyes were stolen. You can say "DNA" but in that case Nagato wouldnt have it so why did the reanimated Nagato and Madara have Rinnegan?
The Summoning: Impure World Reincarnationbinds the soul of a deceased person to a living vessel, restoring them as they were when they were alive in order to do their summoner's bidding.
A reincarnated individual will have all the abilities they had during their life, including kekkei genkai and kekkei tōta. They are physically restored as they were at the time of their death, including any physical handicaps they may have possessed, such as Nagato's damaged legs. Exceptions exist: illnesses they had will not be preserved, nor will any physical damage that contributed to their death. There is some inconsistency of whether or not foreign body matter will be restored as well: Hanzō retains the poison gland of the black salamander, but Madara Uchiha does not have access to Hashirama Senju's genetic material and thus Kabuto must artificially reproduce it for him.
So, Nagato had his eyes at time of death, so as at reincarnation.