No.  Christian doctrine declares that God is the author of life and that He is incapable of making mistakes.  From those beliefs, the only logical conclusion one can draw is that when life exists in the womb, it is God’s will that it be there.  Given that support for legal abortion denies both of these realities, by definition, it is incompatible with Christian belief. 

People who claim to be both pro-choice and Christian are, basically, asserting three things.  The first is that life is not a right inherited from God, but a privilege bestowed by human beings who can withhold it if they “choose” to do so.  The second is that God is neutral on whether a child He created is brutally torn limb from limb.  Finally, they are saying it is possible to reject the innocent new lives which God creates without rejecting God Himself.  From a Christian perspective, these arguments are absurd. 

The bottom line is, a Christian cannot be pro-choice about the intentional destruction of innocent human life any more than they can be pro-choice about rape, robbery, slavery, incest, child abuse, etc.