Microeconomic rationale for UIP (uncovered interest rate parity)

There is an arbitrage argument for UIP because under UIP forward rate must be equal to expected exchange rate so the same arbitrage arguments from CIP can be extended to UIP (under its strict assumptions). You will find it in most international macroeconomics or finance textbooks. For example, according to Nelson Mark's International Macroeconomics and Finance:

If foreign exchange participants are risk neutral, they care only about the mean value of asset returns and do not care at all about the variance of returns. Risk-neutral individuals are also willing to take unboundedly large positions on bets that have a positive expected value. Since $F_{t} − S_{t+1}$ is the profit from taking a position in forward foreign exchange, under risk-neutrality expected forward speculation profits are driven to zero and the forward exchange rate must, in equilibrium, be market participant's expected future spot exchange rate

$$F_{t} = E_{t}(S_{t+1}). (1.6)$$

Substituting (1.6) into (1.2) [result given from covered interest parity where instead of expected exchange rate you have forward rate] gives the uncovered interest parity condition $$ 1 + i_t = (1 + i_t^* )frac{E_t[S_{t+1}]}{S_t}. (1.7)$$ If (1.7) is violated, a zero-net investment strategy of borrowing in one currency and simultaneously lending uncovered in the other currency has a positive payoff in expectation. We use the uncovered interest parity condition as a first-approximation to characterize international asset market equilibrium, especially in conjunction with the monetary model (chapters 3, 10, and 11). However, as you will see in chapter 6, violations of uncovered interest parity are common and they present an important empirical puzzle for international economists.

The in text square brackets contain my clarifications. So as the above passages show there is an arbitrage argument in UIP. You can find further sources and more detailed explanations in the textbook itself.