Is rom a input or output device?

ROM can refer to many things. For example, the full name for a CD is a CD-ROM which stands for compact disc, read-only memory. So it acts as a storage device, and in some mind sets, could be considered input to the computer.

In digital circuits a ROM is often used as a look up table type circuit and is generally something that has several inputs, performs logical operations on those inputs, and outputs the corresponding value(s).

So, the answer to your question? It depends on what you're actually talking about, but it would most easily be defined as neither in the normal sense of input and output devices for a computer. You'll have to define what you are referring to by ROM.