There are actually some scientific evidence that support reincarnation can be real, although I must point out, the evidence are circumstantial.
What we normally refer to as reincarnation scientifically could be the energy transfer of the nerve system.
To explain what I mean, the human brain and nerve and nerve system run on electricity just like all household appliance and it is the same set of energy. This energy source stay with u for life, starting from the moment u are born and only leave when u die and won't increase or decrease during your life.
According to the principle of physic, energy can neither be created nor destroy, but only transfer from one form to another. Thus, the energy used in a human nerve system is from external source, that enter our body, a few months into our mother's pregnancy and would leave our body after we die. Some theory belief our conscious somehow imprint itself into this energy our body use, thus, even after we die, in some manner our conscious remain alive, with the energy source, thus, when this energy source enter a new host body, that conscious of ur, also become a part of that person. Scientists belief this become what we refers to as reincarnation, ghost, soul, spirits and maybe even gods.
In fact in many religion that belief in reincarnation, such as Buddhism. It say souls can split out and then join with other soul to reincarnate into another person, which is in total in coalition with the nature of energy moving from one nerve system to the next.
In addition there are many cases of children recalling memory of another person, totally unrelated to them, which might be an indication of past life memory.
So there are many evidence to support the theory of reincarnation, although it is not enough to prove reincarnation, but is for certain, in favor of the possibility