"to convict quickly and perhaps unjustly," 1873, American English, from railroad (n.).
A person knowing more than might be desirable of the affairs, or perhaps the previous life of some powerful individual, high in authority, might some day ventilate his knowledge, possibly before a court of justice; but if his wisdom is railroaded to State's prison, his evidence becomes harmless. ["Wanderings of a Vagabond," New York, 1873]
Related: Railroaded; railroading. An earlier verb sense was "to have a mania for building railroads" (1847).