If an Asteroid was to strike the Earth, would it affect the Earth's rotation? If an Asteroid was to strike the Earth, would it affect noticeably the Earth's rotation, and if so, how large would this Asteroid have to be?
To have a noticeable effect the impactor needs to be BIG.

Most questions about "what would happen if ... hits" can be answered by the "Earth impact effects program" (http://impact.ese.ic.ac.uk/)

Here are calculations for a 100km stony asteroid... 

A brute like this would have a good chance of wiping out most complex life on the planet. There has been nothing like this in the last 4 billion years (or so)... It could cause the length of the day to change by "up to 2.42 seconds"

As gerrit said, it would be the last of our worries.