The Bible doesn't specifically address this. Unfortunately, The Bible isn't clear on the reason for not marrying your sister, and the idea of non-blood relations isn't addressed. There's actually a chart on Wikipedia matching verses to types if potential incest, and for step siblings, there's nothing.
This is not to say it's O.K. or not. There are plenty of specifics the Bible does not address specifically.
- It does not specifically mention masturbation.
- It does not mention whether or not it's O.K. to buy your wife flowers.
When there is no clear Biblical statement in a moral issue, such things are next determined based on extrapolating Biblical principles.
For the first item in my list, for example, Jesus said if you look at a woman to lust after her, you've committed adultery in your heart. By extrapolating, if you're doing that, you're probably lusting after something, so it is wrong.
For the second, there's no Biblical principle condemning it, so there's no problem.
So the answer to your question remains "there's nothing specifically forbidding it, and genetic similarity isn't cited as the reason for the prohibition on sexual relationships with close relatives." I still don't know if that makes it o.k., though.
Perhaps a better follow-up question that may have more definitive answers, you could ask what is the Catholic view on this, or another denomination...
Next, in some places, marrying a step-sibling is illegal, so the admonition to obey secular authority would apply.
The final test is the test of conscience (which can be seared, so the lack of conviction from your conscience can be deceiving).
The following is my personal take, not a doctrinal take. For what it's worth...:
I have a vague feeling that it's wrong, and most of the time when I have this feeling, and I'm thinking of questions like this, it's like I know it's wrong but am looking for a loophole to get away with it. Once I realize that, I trust my conscience, even though I really want what my conscience tells me is wrong. God gave me a conscience for just this reason.
I can think of dozens of reasons it's a bad idea. What if you break up? How would that affect the parent's relationship? And if you grew up together, it's more than just a little bit more icky. But I'm not sure that's on-topic for this question.