You'd have to cancel out the sideway movement of the earth, and it's going roughly 85000km an hour.
Once you cancel that out, you'll simply fall down to the sun. But you'd need a very powerful rocket. It's way easier to get to mars, as comparison.
It's more realistic to do gravity assists from venus and other bodies, and in that case it'd take years. Just a rough guesstimate would be 10 years I guess? But maybe you'd have to even sling past jupiter or something to really slow down, so then it might be decades.
If the planets line up correctly, you can do it in way less, like 4 or 5 months. I'd need to get some orbital calculations out for the whole thing
But simplest case, you lower your perihel to Venus orbit, that'll take you less than half a year. With a perfect gravity assist you can then head straight for the sun at more than orbital speed, accelerating as you go. Free fall time is a fraction of orbit time, and you're going in with a high initial velocity, so a month or two more, max. That's 6-9 months total, but it'll be faster with more Δv