Let's say a new question is posted, and I've answered that question before in depth. If I link to my answer in my comment, would that be considered "promoting" that answer - an attempt to gain more upvotes for that answer? Is it acceptable, or would I receive criticism for doing so, even though it was unintentional?
Is it acceptable to linking our answer?
Yes it is acceptable. It is not considered as self promoting for upvotes. If you think the question is same then you can close/flag the question as a duplicate.
Would that be considered "promoting" that answer?
No. In fact it is considered a good behavior for not posting the same answer twice.