The performance of Link Adaptation (LA) under the influence of inter carrier interference (ICI), which is cause by carrier frequency offset (CFO) and Doppler frequency spread due to mobility, in orthogonal frequency division multiplexing (OFDM) based wireless systems is analyzed in this work. LA maximizes throughput while maintaining a target bit error rate (BER)or Block Error Rate (BLER) at the receiver using the signal to noise ratio (SNR) fed back from the receiver to the transmitter. Since ICI power is proportional to the signal strength, the implications of such an impairment on LA OFDM systems is not obvious and has not received much attention till now. It is seen that when ICI is not captured in the SNR measured then the LA system fails to meet the target error rate. However, it is shown that with suitable modification to the SNR switching threshold for changing the adaptive modulation can over the problem. It is also noted that ICI severely reduces the spectral efficiency of OFDM systems even when LA is used.