Please have a look at [Quora's terms of service](https://www.quora.com/about/tos), more specifically the section **Quora's Licenses to You**, which starts with the words (emphasis added):

> Subject to these Terms, Quora gives you a worldwide, royalty-free,
> revokable, non-assignable and non-exclusive license to re-post any of
> the Content on Quora anywhere on the rest of the web provided that the
> Content was added to the Service after April 22, 2010, and provided
> that the user who created the content has not explicitly marked the
> content as not for reproduction, and provided that you: (a) do **not
> modify** the Content; (b) **attribute Quora by name** in readable text and
> with a human and machine-followable link (an HTML <a> anchor tag)
> linking back to the page displaying the original source of the content
> on http://quora.com on every page that contains Quora content; 
> (c) **upon request**, either by Quora or a user, **remove the user's name**
> from Content which the user has subsequently made anonymous; (d) **upon
> request**, either by Quora or by a user who contributed to the Content,
> make a reasonable effort to **update a particular piece of Conten**t to
> the latest version on http://quora.com; and (e) **upon request**, either
> by Quora or by a user who contributed to the Content, make a
> **reasonable attempt to delete Content that has been deleted or marked
> as not for reproduction** on quora.com. (...)

So you can, under certain specific conditions (please read the entire section "Quora's Licenses to You"), reproduce answers submitted to Quora. As always when you reproduce content that is not your own, it should be very clear what the source is, and what you actually reproduce (by using quotation marks, quotation markup, ...) and what you add of your own. 

However, due to provisions c, d and e, reproducing Quora answsers that are not your own does not look very attractive. 

Update: Added provisions c-e in response to a comment by Tonepoet.