The entire process involves removing specific genes (ieNA) from a donor organism, and inserting this genetic material into the DNA of a host organism, usually a bacteria or virus cell. The whole process is pretty amazing. There is quite a bit more detailed information on the internet...there is also a brief video on YouTube of how the process works if you are interest. I didn't realize it, but one of the first recombinant DNA medications produced was Human Insulin back in the 1970's. Prior to that time, all insulin used was derived from the pig pancreas.

But, to answer your question, while there are no blood fractions involved in the recombinant DNA process, there may be a blood fraction added to the final medication produced. Usually, this will be a small amount of albumin (a protein produced by the liver, but extracted from donated blood). The albumin is used as a stabilizing agent. Not all recombinant products have albumin added, so you will need to ask.