No. The problem is that as you approach the speed of light, your effective mass increases. This is a measured effect that has to be allowed for in particle accelerators where electrons and protons are regularly accelerated to better than 99 percent the speed of light. As the mass of the spaceship increases, so does the inertia of the spaceship and it takes a stronger thrust to keep increasing its velocity by one more kilometer per second. By the time you get really, really close to the speed of light for a rocket ship weighing many kilograms, you have to expend energy at a rate comparable to the output of all the nuclear power plants now in operation. In most designs, you have to bring the weight of the nuclear fuel and the power plants with you too! This adds more weight and so requires even more thrust. The only way out of this is to, 1) use a 'laser cannon' focused on the spacecraft to push it from Earth or 2) use the energy latent in the quantum fluctuations of local spacetime. Both of these are pure science fiction. Alas!