There are several premises to this question:
- Scrimgeour was captured and held in captivity long enough for there to have been an attempted rescue.
This is not necessarily what happened. From Voldemort's meeting with the Death Eaters in the beginning of Deathly Hallows it seems that his plan was to slowly have Scrimgeour surrounded by Death Eaters and then go in for the quick kill:
“It is a start,” said Voldemort. “But Thicknesse is only one man.
Scrimgeour must be surrounded by our people before I act. One failed
attempt on the Minister’s life will set me back a long way.”
This could indicate that they simply killed Scrimgeour on the spot and there was no time for any attempted rescue.
However, later in the book Lupin tells Harry about a rumor that Mr. Weasley heard:
Arthur heard a rumor that they tried to torture your whereabouts out
of Scrimgeour before they killed him; if it’s true, he didn’t give
We don't know whether the rumor is true, and even if it was true, "torturing" could simply have been a couple of minutes of the Cruciatus Curse, after which Voldemort gave up on extracting information from him and just killed him. Thus, there is still the possibility that there was not a large enough timeframe for there to be a rescue.
- There were still enough aurors left to mount a rescue operation.
This, too, is not necessarily true. By this time Voldemort had already infiltrated much of the ministry. In the meeting with the Death Eaters it is even kind of implied that the Auror Office is no longer a threat:
“If he has been Confunded, naturally he is certain,” said Snape. “I
assure you, Yaxley, the Auror Office will play no further part in the
protection of Harry Potter. The Order believes that we have
infiltrated the Ministry.”
“The Order’s got one thing right, then, eh?” said a squat man sitting
a short distance from Yaxley; he gave a wheezy giggle that was echoed
here and there along the table.
This shows us that the Order suspected that even the Auror Office had become compromised, and the Death Eaters confirm that this is true. Thus, there may not have been a team of aurors not under Voldemort's control left to attempt to rescue Scrimgeour.
- Aurors can throw off the Imperius Curse.
This is also not necessarily true. As Barty Crouch Jr. in the guise of Professor Moody said in Goblet of Fire:
“The Imperius Curse can be fought, and I’ll be teaching you how, but
it takes real strength of character, and not everyone’s got it.
Better avoid being hit with it if you can.
It is thus very possible that aurors (some of them at least) cannot throw off the Imperius Curse.
- The auror department is the most elite department in the entire Ministry of Magic.
This one is probably true. At least Ron seems to think so:
“Well, it’d be cool to be an Auror,” said Ron in an offhand voice.
“Yeah, it would,” said Harry fervently.
“But they’re, like, the elite,” said Ron. “You’ve got to be really
good. What about you, Hermione?”
- The Auror Department is under the command of the Minister of Magic.
In the sense that he is the top ranking official of the agency that they are a part of, they are under his command; however, that does not necessarily mean that they are directly under his command on a day-to-day basis. There is a Head of the Auror Department for that. Morevoer, even if the minister could command the aurors it wouldn't help here because you are asking about a situation in which the minister was in captivity, with presumably no way to contact the aurors.
In conclusion, we don't know if Scrimgeour was even held in captivity for any length of time, we don't know if there was even a functioning Auror Department (not controlled by Voldemort) at that point, we don't know that aurors can throw off the Imperius Curse, and we don't know that Scrimgeour had access to command them. In short, we don't have any information that would support the possibility of a rescue operation.