The biggest connection between these two texts in my opinion lies in the way that both concern the creation of life and then the relationship between the creator and their creation. In Frankenstein, Victor labours obsessively over creating a creature and then giving it the spark of life to make it a living being. However, when he has done this, although he has spent so long over trying to achieve this goal, he finds himself strangely repelled and disgusted by the creature, and shuns him.
In Blade Runner, we are presented with various replicants that have been created by Dr. Tyrell. One of the most important scenes of the film comes when Roy takes Sebastian with him to confront Dr. Tyrell and to ask for more life. Roy says the following words when he greets Dr. Tyrell:
It's quite a thing to meet your maker.
Both texts therefore involve the way in which the creator and the creatures that they create meet and face each other and the resulting conflict that emerges with this meeting. In the case of the creature in Frankenstein, he focuses on trying to force his creator to make him a companion. In Roy's case, he tries to get his creator to give him more life. Both creators are unable or unwilling to fulfill the request of their creations, and both suffer as a result.