I have a Canon T2i, and I'm wondering if I can take some IR photos with it.
To an extent yes your camera can support IR photography. It has an IR filter but if you mount a visible light blocking filter on the lens and use a long enough exposure you can record images in infra red.
Alternatively you can have the IR filter on the sensor replaced with a visible light blocking filter and shoot images handheld without anything on the lens.
Without modification, the Canon EOS 550D (Rebel T2i) is not suitable for infrared photography. Even with modification, the sensor stack of some Canon cameras still appears to be insensitive to IR compared with other cameras. There is likely an element, other than the hot mirror, that blocks a significant amount of IR. Based on a diagram in this modification guide, a potential culprit is the low-pass filter.
Even after modification, high-quality IR filters are needed. Any visible light that makes it to the sensor will confuse the camera, and the resulting images will not have bright foliage characteristic of IR photos. The following were taken with a 550D that had the hot-mirror removed.