Yes, you can.
A citizen of a different country (alien) can adopt in Ukraine a child who is a national of Ukraine on the general basis set forth in the Family Code of Ukraine.
A child who is a national of Ukraine may be adopted by an alien if/after the child has been registered at the State Department for Adoption of Ukraine. Such registration must be for a period of one year in order to allow Ukrainian nationals chose this child for adoption. If the adopter is a child’s relative, such adoption may be effected prior to this time-limit.