Wa `alaykum as-Salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, we would like to thank you for the great confidence you place in us, and we implore Allah Almighty to help us serve His cause and render our work for His Sake.
Your sister should realize that Hijab is meant to preserve the dignity of the Muslim woman. Like all other Shari`ah-based commands, Hijab should be given due care, for it brings about countless benefits and wards off a great deal of harm and evil. You must continue to try to convince your sister with these facts using wisdom and good admonition.
In her response to your question, the prominent Muslim scholar and Da`iyah Zeinab Mustafa states:
"My dear brother in Islam, Jazakum Allahu khairan for being such a good brother who wants to protect his sister from going astray. This good intention should also have a good strategy in order to convince your sister to wear the Hijab simply because she loves Allah and not as a duty imposed by a human being.
I do not think that you have the right to impose Hijab on your sister, but your duty is to let her know and feel the greatness of Islam and how important it is to practice it and to choose the way of Allah. I think girls like your sister, do not like to be lectured, so I advise you to find a good group of Muslims who organize some Islamic activities and encourage your sister to attend so that she will love Islam and the Muslims. This will give her a chance and help her to learn about Islam.
Try your best to teach her some surahs from the Qur’an and the meaning of the Sunnah and help her to increase her belief in Islamic values and culture. To order your sister to wear the Hijab does not help at all, but to enable her to understand Islam and to inspire her to develop her faith in her heart is a great effort. You have to start by loving your sister, respecting her, showing kindness to her, spending time talking to her, and not ordering her to wear it."
Finally, make du`a' (supplication) for her that Allah guides her to the straight path!
You can also read:
A Wife Not Convinced of Wearing Hijab
Hijab: Always A Woman’s Business?
Does Hijab Infringe upon Women’s Liberty?
Can Muslim Parents Force Hijab on Daughters?
Hijab, Why?
Hijab : A Clear Vision