Step 1: Understand Hinsberg's reagent.
Hinsberg's reagent is benzene sulphonyl chloride (C$_6$H$_5$SO$_2$Cl). It is used in the Hinsberg test for the identification of amines.
Step 2: Analyze the options.
- Benzene sulphonyl chloride (Option A) is the correct answer as it is the Hinsberg reagent used for testing amines.
- Benzene sulphonic acid (Option B) is a different compound used in other reactions.
- Ethyl oxalate (Option C) is not involved in the Hinsberg test.
- Acetyl chloride (Option D) is used in the preparation of acyl derivatives but not in the Hinsberg test.
Step 3: Apply to the options.
The correct answer is (A) Benzene sulphonyl chloride.
Final Answer:
\[
\boxed{\text{Benzene sulphonyl chloride}}
\]