According to his eminence Ayatullah Sistani: yes, they can get married after this but first the girl must repent on the sin committed. Also, the child will be
illegitimate for the rest of his/her life.
For more reference pls visit the Q&A session on www.sistani.org under the title 'adultery'
"... verily Allah is the best of the forgivers"...-Holy Qur'aan