It is I who am/is to blame

It is I who is to blame is correct.

Yes, agreed, but the phrase is so awkward-sounding it would be better to try something different.

Personally, my view is that if you like applying Latin rules to English grammar you would prefer the following, which is correct English:

It is I who am at fault.

If you disagree with that, you would prefer

It is me who is at fault.

Or if you wished to be annoying, you could mix them, but at least be aware of the difference and where it comes from.

Hooboy. I'm staying out of this.

It has nothing to do with correct. Before you can decide that MsTan, you've gotta the register you want.

More formal

A: Who is to blame?
B: It is I/me who is to blame.

More colloquial

A: Who's to blame?
B: It's me who is/who's to blame.