Recently, extensive research has focused on addressing the unique challenges of smart contract fuzzing. Nevertheless, existing fuzzers still struggle to generate adequate function call arguments that can explore the deep smart contract states. In this paper, we introduce novel classes of argument constraints that capture the inter-argument relationships required to exercise meaningful contract logic. We propose a static analysis algorithm to extract these constraints from Solidity source code. In addition, we design a constraint-aware argument mutation strategy that leverages the identified constraints to guide test case generation for smart contract fuzzing. We implement our approach in a fuzzer named IConFuzz. Our evaluation on realistic benchmarks with integer overflow, suicidal contract, and ether leakage vulnerabilities demonstrates that IConFuzz outperforms state-of-the-art testing tools in both the number of bugs discovered and the speed of bug detection.