Matthew 1:18-25
Luke 1:1-2:20

"...and her husband Joseph, being a just man and unwilling to put her to shame, resolved to divorce her quietly(Matthew 1:19)."

The theory that Mary was raped by a Roman soldier requires a greater stretch of the imagination than calling the entire virgin birth account a made up story. Although conspiracy theories are attractive to many, this one fails to reflect how real people actually behave. If Mary made up the story about the virgin birth, she should be considered the worst liar of all time. If you're going to tell a lie about why you're pregnant, you're not going to make up some unbelievable story about angels and having God's baby.
1. Regardless of how bad science may have been in that day and age, even an idiot would know when his fiancee is pregnant, and understand that something is amiss if he never actually slept with her. Even in a culture with primitive science, a man is not going to believe his fiancee when she tells him she's pregnant with the son of God. In terms of lies, it's not a very good one.
2. In that day and age, the testimony of women was disregarded in all legal proceedings. She therefore had no reason to believe her story would be accepted.
3. Making up a story like that would make you guilty of blasphemy, which carried a death sentence in that era.
4. Joseph would have more to gain in saying that his child (even if it's another man's child) is his biological son, than to say that the child is adopted (especially adopted from God). The whole Davidic lineage is at stake. If he claimed the child as his natural descendant, he could at least attempt to claim royalty. Saying the adopted child is his own blood would have made it easier for the child to become king of the Jews.
There were no paternity tests back then, so Joseph could have claimed another man's baby as his own if he wanted. If he wanted to lie about something, he should have lied and said the child was his, not tell people some unbelievable story about a virgin birth.
5. Joseph is described as a "just man" who was "unwilling to put her to shame," but decided to divorce her quietly. In other words, he wasn't going to stone her to death for adultery. Wouldn't it make more sense for her to tell the truth and beg him not to leave, rather than make up a wild unbelievable story?
6. The New Testament says that Joseph remained betrothed to Mary due to receiving a message from an angel. Since they stayed together, if the child was born from another man, it would have made more sense for them to just lie and say the child is theirs, as explained in point 4.
7. Telling people your wife was raped by a Roman soldier would be a great way to stir up a rebellion against the Roman government. In fact, if Joseph heard about something like this, he probably would have gotten involved with rebels trying to overthrow the government. But that's not in the bible at all, despite how dramatic it would have made the story.
8. If this argument was merely to discredit the concept of Jesus being the Son of God, making Joseph the biological father would have been sufficient. Of course, then he'd still be the messiah because he's a descendant of David. It's likely that a rabbi came up with the rape/adultery theory for that reason (but it takes an extra step of the imagination).
Oddly enough, these alternative theories came out about a hundred years after the first church was established, rather than during the life of Jesus (when they'd be relevant).
In summary, either the account of the immaculate conception is true, or it isn't. An weird alternative theory with the flavor of truth isn't evidence that the original account is false. That kind of thing works just as well as theories that we faked the moon landing.
As unbelievable as it sounds, Mary, a virgin, had a child without sleeping with anyone. And the child was the Son of God. Mary and Joseph had absolutely nothing to gain from telling this story, but they told it anyway, and it's been passed down for generations as absolute fact.
Even after his birth, Jesus showed himself to be divine through his actions, his words and his miracles. Having a birth with no human origin only serves to prove that his words, his power came directly from God.

Dear Father in heaven, thank you for sending your Son Jesus into the world to save us from our sins. Lord, your word is being challenged, questioned and denied every day, but nothing can destroy it. Please shine the light of your truth into the darkness of this world. Please destroy the lies and accusations, and help us, your people, to stand firmly grounded in the truth, so that the darkness doesn't overwhelm us. Please lead us to your truth, Lord. I pray this in your Son Jesus' name. Amen.