1. The fine-tuning of the universe's initial conditions is either the result of chance, necessity or design. (Premise)
2. It is not due to chance or necessity. (Premise)
3. Therefore, it is due to design. (From 1 and 2)
Surely this argument is rationally acceptable. Other philosophers, such as Robin Collins, maintain that this is a rationally compelling argument, but I won't get into the science of the argument. I'm simply not qualified as a philosopher and theologian to enter into a scientific debate. Nevertheless, neither premises (1) or (2) are obviously false. In fact, (1) is appears to be obviously true, barring any additional (and currently unknown) alternative.
I prefer the argument from order:
4. Whatever exhibits regularity is not the result of chance alone. (Premise)
5. The laws of nature exhibit regularity. (Premise)
6. Therefore, the laws of nature are not the result of chance alone. (From 4 and 5)
(6) leaves the possibility of nature's regularity being the result of necessity or design as an open question. I'm happy to leave this as an open question. In fact, the theist may use the argument from order as one part of a cumulative case for God's existence. One might combine the argument with the argument from reason, for example.