No, its blasphemy. Christians shouldn't perform yoga. The American Institute of Vedic studies by David Frawley is quite determined to bring out the misconceptions that many of them have on Hinduism and Yoga.
Hiranyagarbha and Vedic Yoga
Who then was Hiranyagarbha, a human figure or a deity? The name Hiranyagarbha, which means “the gold embryo”, first occurs prominently as a Vedic deity, generally a form of the Sun God. There is a special Sukta or hymn to Hiranyagarbha in the Rig VedaX.121, which is commonly chanted by Hindus today. The Mahabharata speaks of Hiranyagarbha as he who is lauded in the Vedic verses and taught in the Yoga Shastra (Shanti Parva 339.69). As a form of the Sun God, Hiranyagarbha can be related to other such Sun Gods like Savitri, to whom the famous Gayatri mantra is addressed. Therefore, the Hiranyagabha Yoga tradition is a strongly Vedic tradition. We can call it the Hiranyagarbha Vedic Yoga tradition.
Krishna states in the Bhagavad Gita (IV.1-3) that he taught the original Yoga to Visvasvan, another name of the Sun God, suggesting Hiranyagarbha. Vivasvan taught this Yoga to Manu, the original man or first king, making it into the prime Yoga path for all humanity.
As it clearly states Yoga is owned by the Sun God, it is no ones intellectual property. It was he who gave the knowledge of yoga to the world and yet the world is totally ignorant of this and gives no homage to him. (Hindu Group Stirs a Debate Over Yoga’s Soul - New York Times)
What most westerners don't understand is that it is impossible to separate the Vedic deities from the practice of Yoga. Vedic deities are anthropomorphic gods with whom we can have a dialogue with, they are real beings and they reside in our bodies, this is the traditional view and we will not tolerate if a false interpretation of our scriptures is promoted all over the world.
All those Christians who practice yoga are already worshipping a different image of god. It is wrong as many of the bishops blindly say that Yoga is the work of the devil (Yoga is the work of the devil says Vaticans chief exorcist) without being aware of its origins and the traditions it come from and it is equally wrong to impose Yoga on young Christian minds and try to bring down Christianity.
Christianity doesn't need any help from Hinduism, it is self sufficient, it has all the goods with in it. It has more hope than Hinduism. I'll be more than happy if Christians worship Christ rather than meddling with eastern religions.