it is not a TM its a hm you can get it in Kanto. after you beat the 8th gym leader once you walk out the gym prof. oak will call you and tell him to come to his lab in pallet town to get a gift he he will give you the hm and unlock mt. silver but you have to defeat all gyms in Kanto.
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you get it AFTER you beat blue
You can get Rock Climb from Professor Oak after you've beaten all 16 Gym Leaders.
you get it from oak after beating blue
while you go to snowpoint city there will be a house a little above it theres a pokeball and it is actually rock climb.
Route 211 you need rock smash and rock climb!