Step 1: Subject–verb agreement.
The sentence begins with "It is I...", where "I" is the subject. The verb form following "who" must agree with the antecedent, which is "I." Therefore, the correct verb form is "am."
Step 2: Evaluate each option.
\begin{itemize}
\item (A) It is I who am responsible for this fiasco.
✔ Correct. "I" is the antecedent of "who," so the verb should match "I" → "am."
\item (B) It is myself who is responsible for this fiasco.
✘ Incorrect. "Myself" is a reflexive pronoun and cannot be used as the subject complement here.
\item (C) It is I who is responsible for this fiasco.
✘ Incorrect. Verb "is" does not agree with "I."
\item (D) It is I who are responsible for this fiasco.
✘ Incorrect. Verb "are" does not agree with "I."
\end{itemize}
Step 3: Conclusion.
Thus, the only grammatically correct choice is option (A).
Final Answer:
\[
\boxed{\text{It is I who am responsible for this fiasco.}}
\]