Can abdominal aortic aneurysm cause fast heart rate and palpitations?

Not really: The presence of an aneurysm itself shouldn't cause cardiac symptoms. If it were to rupture there would certainly be cardiac issues, but these would probably be overshadowed by the intense pain from the rupture.

Typically no: There are usually no symptoms from an abdominal aortic aneurysm, except a palpable, pulsatile mass in the abdomen. If an aneurysm bleeds, this is a completely different picture with many additional symptoms, like abdominal pain, fast heart rate and possibly palpitations.

Unlikely: The natural history of AAA is that they enlarge and rupture. AAA are usually asymptomatic until they leak and/or rupture. At that point, along with severe back or abdominal pain, one could have a rapid heart rate and palpitations as a sign of hemorrhagic shock. So, it is unlikely that a AAA would cause these symptoms.