Does Islam force Muslim women to wear the Hijab (the headscarf)

Islam does not force anything upon any person but God does point out that the one who rejects evil and choses the right way will be successful. 

There is no compulsion in religion. The Right Way stands clearly distinguished from the wrong. Hence he who rejects the evil ones and believes in Allah has indeed taken hold of the firm, unbreakable handle. And Allah (Whom he has held for support) is All-Hearing, All-Knowing. (Quran 2:256)

God does tell the believing women to cover their heads and their bodies and not to reveal their adornments other than to those to whom it is permissible. 

God has warned us in the Quran, the Bible and the Torah against satan who will lead us into temptation in committing sin so it is upon us as believers to take the guidance that God has given us so that we remain on the straight path but the choice is ours to chose our own paths.

The Bible warns us about Adulators women and how they dress with clear intent to do evil. 

Proverbs 7-9

Warning Against the Adulterous Woman

7 My son, keep my words
    and store up my commands within you.
² Keep my commands and you will live;
    guard my teachings as the apple of your eye.
³ Bind them on your fingers;
    write them on the tablet of your heart.
⁴ Say to wisdom, “You are my sister,”
    and to insight, “You are my relative.”
⁵ They will keep you from the adulterous woman,
    from the wayward woman with her seductive words.

⁶ At the window of my house
    I looked down through the lattice.
⁷ I saw among the simple,
    I noticed among the young men,
    a youth who had no sense.
⁸ He was going down the street near her corner,
    walking along in the direction of her house
⁹ at twilight, as the day was fading,
    as the dark of night set in.

¹⁰ Then out came a woman to meet him,
    dressed like a prostitute and with crafty intent.
¹¹ (She is unruly and defiant,
    her feet never stay at home;
¹² now in the street, now in the squares,
    at every corner she lurks.)

The Bible also gives clear guidance on how to dress and for a women to cover hear head;

1 Corinthians 11:5

But every woman who has her head uncovered while praying or prophesying disgraces her head, for she is one and the same as the woman whose head is shaved.

1 Corinthians 11:10

Therefore the woman ought to have a symbol of authority on her head, because of the angels.

1 Timothy 2:9-10 “Likewise, I want women to adorn themselves with proper clothing, modestly and discreetly, not with braided hair and gold or pearls or costly garments, but rather by means of good works, as is proper for women making a claim to godliness.”

In Islam the term “Hijab” means curtain, separation, wall and, in other words, anything that hides, masks and protects something.

One has to ask, why do you put a cell phone cover on your phone? To protect it from damage. Why do engines have covers over it? To protect the engine from dirt and dust going into it and causing damage to it? In the same way God is trying to protect women when he instructs them to cover their hair and adornments. These are things that men stair at and causes lust. Benefits of wearing Hijab:

1. To identify as being a Muslim
2. Gives the women power – shows that she will not be judged by her looks and that there is more to hear.
3. Shows that she is a women of enormous strength, courage and integrity.
4. She tells people that she does not tolerate disrespect
5. She is not someone to be toyed with.
6. She is religious and shows her submission to God.
7. She is not a sexual object 
8. Sign of modesty
9. Show she is a truthful women, someone that can be trusted.
10. She will not cheat, she will not steal or deceive you.