4) "Your call will be answered in turn" is, I think, the best solution.

1) "Your call will be answered in the order (in which) (it was) received" is terrible English, as shown by others here, because clearly an order refers to a series of things, not one single thing.

2) "Calls are answered in the order received" is correct English, but to appear personal, companies want to tell you about "your" call, not just calls in general.

3) "We answer calls in the order received" is also correct English. This option not only has the same problem as (2) above, but is even worse because the company becomes the subject of the sentence by the use of active voice. So this makes the sentence primarily about the company, rather than your call.

4) "Your call will be answered in turn" is, I think, this is the best solution.