The short answer: yes, you can! The long answer: using an alt-az mount for astrophotography can have its limitations. If you're just looking to take images of bright objects within the solar system, such as the moon and planets, then an alt-az mount will be a good choice.
If you're hoping to take images of deep sky objects, this is where alt-az mounts reach their limits. Depending on your camera and your telescope's focal length, an alt-az mount can track the night sky for up to 30 seconds or so before star trails start to occur. This is long enough to capture some of the brightest deep sky objects like the Orion Nebula, but is not long enough to capture most deep sky objects, which are very faint.