Biblically, there is a lot of translating/inferring to "prove" that God is against abortion, however, that doesn't mean it is wrong because we do that in a vast majority of situations. The most common anti-abortion verse is in Jeremiah 1:5 where it says, "Before I formed you in the womb I knew you." Clearly God is against murder and the taking of an innocent life, especially by conscious decision or actions and then the logical progression is that if God calls us a person before we are even in the womb, than a fetus is a person and worthy of protection.
God has also clearly allowed for exceptions to rules in many situations where things are less black and white. The OT Jewish law attempted to prescribe a rule through rabbinical teaching to almost every situation. Similar to our American rules based legal system, it gets bogged down in a lot of detail and becomes untenable at times. In the NT, Jesus points out the impossibility of obtaining perfection (aka, righteousness) through adherence to the law and provides for grace to obtain righteousness.
In all of this, the rules are still the same, we just can relax about being perfect and be lead by love instead of black and white legalism. But still morality is important to God and the protection of those who can't protect themselves is a part of that. Abortion because you are just starting to get ahead in your career and don't want to disrupt that is clearly immoral Biblically. Abortion because you are a 16 years old and don't want the disruption to your life, the stigma of being pregnant at school, the physical effects of pregnancy and the emotional struggle of giving the baby up for adoption are a little more understandable, but still Biblically immoral. Abortion because your life is in danger during pregnancy or because it is the result of rape is where things change and I personally believe the only morally justifiable reason is due to health risk of the mother. Even in rape I personally wouldn't do it, but I would never make a law or tell a woman she had to carry a baby that was the result of a rape.
So, in answer to the OP....it depends, but in the vast majority of situations, I'd say no. While there isn't exactly a verse in the Bible that explicitly states a fetus has a soul and is a person, it seems to indicate that is the case. They would therefore be subject to the same moral protection as a baby that was just born.