There aren't really enough parameters specified in the question to guide an answer (as can be seen by the variety of responses, ranging from slow mechanical interventions to planetoid collisions).
In general, the Earth can be considered a very-high-efficiency gyroscope with monumental rotational momentum.
@Yakk mentioned E29J energy of rotational momentum. (I assume he means 1 x 10^29 Joules). That's 100,000,000,000,000,000,000,000 Joules. When he says it would take 100 seconds of the Sun's energy output to offset the Earth's rotation, he's not talking about the energy at the surface of the earth; he's talking about all the energy you would trap if you had a shield that surrounded the entire sun, at the sun's surface, for 100 seconds. That shield would have a surface area equal to the sun, which is 12,000 times the surface area of the Earth. And the sun is actually putting out about 3.8 x 10^26 J/s, according to NASA's Sun Fact Sheet. So, you'd actually need a little over 250 seconds of output from the Sun. If you were willing to accumulate the equivalent energy from a smaller source over a month, you could go for another star that only radiated 1/10,000th of the Sun's output (a red dwarf would be handy, I suppose).
Then you'd have to collect that output (all of it), and transfer it to your Earth-tilting mechanism. Alternatively, if you wanted to use the Sun's energy, but were only willing to gather the energy near the Earth, if you were able to build a collector with a surface about the size of the Earth and put it at a Lagrange point ahead of or behind the Earth in the same orbit, then it would take only... 1,252 years to collect all the energy you'd need from the Sun. That's assuming you had 100% efficiency in all of the processes from collecting to transferring the energy, conversion into motion, etc. Make it 2,000 years, for good measure.
I hadn't thought it would be necessary (or useful) to calculate the equivalent in nuclear material that would be needed to create the same effect, but just for grins, here goes:
A megaton is 4 x 10^15 Joules of energy. The Sun outputs about 7.9 x 10^15 megatons of energy a day. 250 seconds' worth would be 22.9 x 10^12 megatons. That's 22.9 quadrillion megatons. I regret to inform you that the entire nuclear stockpile of all of the signatories to the Nuclear Proliferation Treaty amounts to only about 200,000 megatons. To get enough nuclear material, we'd need all of the nuclear material from 115,000,000 (yes, that's millions) Earths.
So, in hard science terms, there's no obvious alternative source of energy other than a planetoid that would accomplish this task, and as you've heard, a planetoid would make a pretty mess of the planet in the process.
Have you considered just finding one such planet and settling it? The time and energy expenditure would be miniscule in comparison... Or just make up a fantasy solar system where the planet already exists; lots of others choose this route to reach an otherwise-implausible context.