You mean a car battery. Yes, you can, but there are some real problems with doing this.
-You would need at least TWO large car batteries connected in *series* to weld. A single battery only produces 12 volts which isn't enough to strike an arc.
-You can't control the current (aka amperage) with batteries. Therefore you have no control over the heat in the weld.
-The current will quickly decrease after less than a minute of welding.
-Car batteries are not designed to be discharged to their full capacity on a regular basis. After fully discharging them six or seven times repeatedly, they will be ready for scrap.
For people that have claimed safety concerns, welding would not discharge the batteries any faster than, for example, hard starting on a cold day.