No, this command does not condone rape. In fact, this act was meant to protect women.
Let’s examine the specific context surrounding this verse. Stating in verse 23, we see that the next couple verses refer to specific circumstances surrounding rape.
If there is a betrothed virgin, and a man meets her in the city and lies with her, then you shall bring them both out to the gate of that city, and you shall stone them to death with stones, the young woman because she did not cry for help though she was in the city, and the man because he violated his neighbor’s wife. So you shall purge the evil from your midst. “But if in the open country a man meets a young woman who is betrothed, and the man seizes her and lies with her, then only the man who lay with her shall die. But you shall do nothing to the young woman; she has committed no offense punishable by death. For this case is like that of a man attacking and murdering his neighbor, because he met her in the open country, and though the betrothed young woman cried for help there was no one to rescue her. “If a man meets a virgin who is not betrothed, and seizes her and lies with her, and they are found, then the man who lay with her shall give to the father of the young woman fifty shekels of silver, and she shall be his wife, because he has violated her. He may not divorce her all his days.
Deuteronomy 22:23-29 ESV
Here we see several different instances of rape. What’s important to note is that it takes into account the woman’s ability to cry for help and resist the circumstances she is put in. Look at the first command, and notice how the first command says the woman was able to cry out for help, implying the woman acted consensually.
In the circumstances you mention, the women is mentioned as “being found”, which is a bit ambiguous, but probably implies that the woman consented.
The way Israel’s culture was at the time required women to be virgins prior to marriage. So what this command is doing is guaranteeing this women a husband. Because if she was raped and not forced to marry the man, she would be destitute, unable to be married in the future.
What the man is doing by paying the father is paying him a bride price, which was a common practice in normal marriages. So this man is essentially forced into marriage for his crime, with no opportunity for divorce.
In this, we see a command that seeks to preserve a form of marriage sanctity when a great evil is committed, so no, this verse does not condone rape.