Do railway tracks get magnetised when trains run on tracks?

No, however some trains have a magnetized wheel to help grip the track.

*Added -

Electric trains do result in short term magnetizing of the train tracks. This can be seen on sharp curves where tiny rail slivers cling along in a magnetic pattern. In the US, trains do not have magnetized wheels, but rapid trainsit systems can include a track brake that uses a magnet to provide much faster braking than the wheels alone.