Events containing one or more top quarks produced with additional prompt leptons are used to search for new physics within the framework of an effective field theory (EFT). The data correspond to an integrated luminosity of 41.5 fb^-1 of proton-proton collisions at a center-of-mass energy of 13 TeV at the LHC, collected by the CMS experiment in 2017. Limits are placed on 16 dimension-six operators by performing a simultaneous fit to the data of the corresponding Wilson Coefficients (WCs) that parameterize the effects of the EFT operators. Two standard deviation confidence intervals for the WCs are extracted; the standard model expectations for the WC values are within these intervals for all WCs probed.