No.
No ! From MedicineNet :
Birth defects are structural or functional abnormalities present at birth that cause physical or mental disability. They are the leading cause of death for infants during the first year of life. Birth defects may be caused by genetic problems, problems with chromosomes, or environmental factors
Such a god would, of necessity, have decreed that the elements of his creation would behave in certain ways relative to each other. Apply heat to water it will become steam; apply cold and it will become ice. These are the laws of nature and Divine intervention (miracles) would require him to break his own rules.
So the tumbling dominoes fall in compliance with those laws and we cope with them the best way we can.
If, for whatever reason, there is a genetic hiccup along the way, birth defects may occur. (Go see Rooster Cogburn's excellent answer.) It has nothing to do with a hypothetical God. It's just the inexorable process of natural law. Sometimes the effect ain't pretty, but we need to find ways to cope.
Imaginative people will adapt by any means they can devise. Unimaginative people blame "God".
I hate Anonymous questions, but this one deserves an answer
Do you really think a loving God would allow things like Birth defects? Babies are the innocent ones in this world.
No, many things cause defects including environment and genetics.
If there is any god at all, then yes, he is responsible. Parents couldn't possibly be to blame for a gene they knew nothing about. Since that's the case, the only possible one to blame would be him.
You are the god you seek.
Believe and Receive.
No, God cannot be blamed. He created the first pair of humans perfect, for all his work is perfect. (Deut. 32:4) When our first parents sinned, not only did they become imperfect and pay with their lives, but all their offspring since then have been born imperfect and in a dying state. (Rom. 5:12) The nature of these imperfections has a bearing on whether a child is born defected.
The good news is that the Bible also tells us that “God is love” and that he has made provision for humankind to regain its perfection by means of the ransom sacrifice of Jesus Christ by means of God's Heavenly Kingdom. Under the rule of that kingdom, there will come to be no tears, mourning, pain or death—hence liberation from all physical and mental defects will no longer exist.