This question comes up as regular as clockwork in our lovecyclingsg Facebook page. At first I must admit I was a bit peeved but then perhaps it's because its called "Road tax" which doesn't really help matters.
More on the user opinion here.
And here's the reason why not and posting it here so its easier to find the next time.
"As the Land Transport Authority (LTA) clarified in 2013: "Public roads are intended to be used by all road users, including cyclists and pedestrians. They are built and maintained using public funds collected from general taxes, including those who do not use motorised vehicles."