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Tangle is a distributed ledger technology that stores data as a directed acyclic graph (DAG). Unlike blockchain, Tangle does not require dedicated miners for its operation; this makes Tangle suitable for Internet of Things (IoT) applications. Distributed ledgers have a built-in transaction rate control mechanism to prevent congestion and spamming; this is typically achieved by increasing or decreasing the proof of work (PoW) difficulty level based on the number of users. Unfortunately, this simplistic mechanism gives an unfair advantage to users with high computing power. This paper proposes a principal-agent problem (PAP) framework from microeconomics to control the transaction rate in Tangle. With users as agents and the transaction rate controller as the principal, we design a truth-telling mechanism to assign PoW difficulty levels to agents as a function of their computing power. The solution of the PAP is achieved by compensating a higher PoW difficulty level with a larger weight/reputation for the transaction. The mechanism has two benefits, (1) the security of Tangle is increased as agents are incentivized to perform difficult PoW, and (2) the rate of new transactions is moderated in Tangle. The solution of PAP is obtained by solving a mixed-integer optimization problem. We show that the optimal solution of the PAP increases with the computing power of agents. The structural results reduce the search space of the mixed-integer program and enable efficient computation of the optimal mechanism. Finally, via numerical examples, we illustrate the transaction rate control mechanism and study its impact on the dynamics of Tangle.