Oh, an actual fanfic about the anime! How long has it been?
And it has a nice little premise. One that should have been explored more over the years.
A few errors with wording and grammar:
This one is small, but sense Team Rocket is an organization and not a place, you use "in" over "at."
Also, most of this entire paragraph is a cavalcade of run-on sentences. You should replace a few of those commas with periods.
*you're - One of the most common mistakes on the internet though, lol.
“Rhyperior, hammer arm go! Ash, I let you beat me last time. You walked into my trap this time and I will crush you!”
Rhyperior sprung out of the pokéball that Giovanni had been fiddling with and charged at Pikachu. For a Pokémon of such large bulky size this Rhyperior was shockingly fast. Its right forearm smashed into Pikachu knocking him backwards toward Ash.
“Ash, it is no use!” Giovanni chuckled. “Both of you will not leave here unless you join me!”
All around, it's nice and creative minus the glaring grammar and spelling problems.
My only advice would be to knock up the intensity. Ash is joining a criminal organization here. He needs to feel the pressure of every decision he makes and it's up to you to interpret that properly.
Keep up the nice work. You have a fan in me.