In The Kite Runner, could it be said that by telling Amir about her affair with the Afghan man, Soraya is taking responsibility for her...

This would be a very good example of someone taking
responsibility for their actions. This section of the novel comes in Chapter Twelve,
when after the engagement has been arranged by Baba, Soraya calls up Amir and tells him
about her past. What is important about this phone call is that this comes at the
beginning of their formal relationship, and, as Soraya says, she doesn't want their
relationship to "start with secrets." The revelation that follows - that Amir had
actually heard about from Baba - shows Soraya's remorse at what she has done, but also
the way that now she is able to thank her father for what he did in rescuing her from
that situation.

Of course, what you need to be aware of is
how the author uses Soraya as a foil for Amir here. The last paragraph of this chapter
makes this clear:

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I envied her. Her secret was out. Spoken. Dealt
with... I suspected there were many ways in which Soraya Taheri was a better person than
me. Courage was just one of
them.

So, yes, this example
shows Soraya taking responsibility for her actions, in a way that Amir has yet to
do.