Well, strictly speaking we could do that right now.
In fact, NASA has already sent 5 probes completely out of the solar system. Look up the following:
http://en.wikipedia.org/wiki/Voyager_program
http://en.wikipedia.org/wiki/Pioneer_10
So there is no reason why we could not design a suitable trajectory to send a probe to A cent.
The only problem is that with the best current technology, it will take around 150,000 years to get there! But if your purpose is simply to send a human artifact to another star, you will have succeeded. Check this:
http://en.wikipedia.org/wiki/Voyager_golden_record
Apart from such missions, it is conceivable that if enough budget was available we might build something like this:
http://en.wikipedia.org/wiki/Project_Daedalus
It would use a more exotic form of propulsion such as ion drive, or if we were desperate enough nuclear rocket technology is available. The transit time could possibly be reduced to several thousand years. If the probe send back signals of what it found, it is remotely possible that whatever species takes over from humans might be able to receive the signals in (say) 20,000 years time.
Cheers!