Does An Ink Pen Work In Zero Gravity?

Yes. The first was the Fisher space pen designed by pen company, Fisher in the 1960s for NASA's forays into space and to the Moon. Since then the Fisher space pen has become a permanent feature of NASA Apollo, Skylab and Shuttle missions as well as the Russian Soyuz space program, the MIR space station and the European ARIANE space flights.

The problem set for pen manufacturers by NASA in the early 1960s was to develop a reliable pen that would write in the gravity-free environment of space and at any angle. As luck would have it, Fisher already had most of the answer sitting on its work bench in the shape of the Universal Refill. This development involved the use of a semi-solid ink that flowed only when the shearing action of the rolling ball liquefied it.

After more R&D work, Fisher found that by adding pressurized nitrogen gas to the ink cartridge, the pen no longer required gravity to write normally and could do so from any angle of orientation.

A normal ink pen would not, but the pens designed specifically for 0-G will work.
Although, if you plan on going into space, I suggest you use pencils instead. They won't blot or anything.