This paper analyzes the effect of operational amplifier (OPAMP) input offset on continuous-time (CT) delta-sigma (Delta Sigma) modulators with current-mode feedback digital-to-analog converters (DAC). Our analysis shows that the input offset leads to either increased harmonics or increased noise floor of the modulator, depending on whether a DAC shuffling scheme, such as data-weighted averaging (DWA), is applied or not. Analysis and mathematical derivation are given and verified by transistor-level simulations. An input-offset cancellation scheme is proposed and demonstrated by simulation results.