You ask an important question: Can a Christian practice martial arts? My immediate answer is yes, with caution. There are many types of martial arts, and of course, some are wrapped up in Eastern mysticism and therefore should be shunned.
However, not all marital arts are religious in nature. There is nothing wrong with a Christian being a soldier, or being trained and prepared to defend themselves. In fact the Westminster Confession of Faith requires all lawful studies and endeavours to preserve life and property. (See Faith and Firearms article).
Also I have written on this in our The Christian at War booklet.
My 20-year old son, Christopher, is a senior black belt in Karate and has represented our country overseas and recently brought back two bronze medals from Switzerland.
We most certainly, as God-fearing, Bible-believing Christians, investigated the branch of martial arts that he was interested in first before allowing him to participate. We are confident that it has no religious connotations of Eastern mysticism attached to it, but is purely an exercise and a martial art for self-defence.
That obviously is not so for all branches.
However, you should be observant, discerning and ask probing questions. If there is any meditation, incense, statues and the like, then it would be best to avoid it.
If it is merely physical and encouraging disciplined focus that is good for exercise and self-defence then it may be participated in.
May God continue to be your joy and strength.
Yours for Faith and freedom
Dr. Peter Hammond