My understanding is that the current normal AncestryDNA product, which tests Autosomal DNA, does not include the Y-DNA or mtDNA SNPs that would be useful for determining your haplogroup(s).

Ancestry sells separate, more expensive DNA tests for Y-DNA and mtDNA:

http://ldna.ancestry.com/buyKitGoals.aspx

(Their competitors offer similar tests, so it might be worth shopping around.)

Assuming Ancestry doesn't do the work for you and present a pretty graph or what have you with the results, you would likely be able to download the raw data and figure out the haplogroup yourself using the ISOGG's database:

http://www.isogg.org/

My understanding is that the current normal AncestryDNA product, which tests Autosomal DNA, does not include the Y-DNA or mtDNA SNPs that would be useful for determining your haplogroup(s).

Ancestry previously sold more expensive DNA tests for Y-DNA and mtDNA, but no longer do. FamilyTreeDNA does, however:

https://www.familytreedna.com/

You'll need to download the raw data and figure out the haplogroup yourself using the ISOGG's database:

https://isogg.org/tree/index.html