The simplest answer if you're dealing with short recordings is to listen to it and detect "pops" (short spiked sound) in the playback. However, a more robust solution is to analyze the frequency spectrum of the recording.
Recall that when a signal gets clipped at some threshold, it locally resembles a square wave in the clipped regions. This introduces higher harmonics in the frequency spectrum which would not have been there originally. If your signal is bandlimited (most real world signals are) and you're sampling well above the Nyquist rate, then this stands out quite clear as day.
Here's a short example in MATLAB demonstrating this. Here, I create a bandlimited signal of 1s duration, sampled at 1000Hz, and then clip it to between
±0.8 (see the top plot in the figure below)
time = 0:0.001:1;
cleanSignal = sin(2*pi*75*time).*chirp(time,50,1,200);
clippedSignal = min(abs(cleanSignal),0.8).*sign(cleanSignal);
You can clearly see that the frequency spectrum of the original, unclipped waveform is clean and goes to zero outside the bandwidth (bottom left), whereas in the clipped signal, there is a general minor distortion of the spectrum (expected if clipped) and most importantly, higher harmonics/spikes/non-zero contributions in the spectrum outside the bandwidth of the signal (bottom right).
This might generally be a better approach, because detecting clipping by looking at the values is generally not accurate unless if you designed the equipment yourself and know precisely the value of the threshold.