Inference of causality between gene expression and complex traits using Mendelian randomization (MR) is confounded by pleiotropy and linkage disequilibrium (LD) of gene-expression quantitative trait loci (eQTL). Here, we propose an MR method, MR-link, that accounts for unobserved pleiotropy and LD by leveraging information from individual-level data, even when only one eQTL variant is present. In simulations, MR-link shows false-positive rates close to expectation (median 0.05) and high power (up to 0.89), outperforming all other tested MR methods and coloc. Application of MR-link to low-density lipoprotein cholesterol (LDL-C) measurements in 12,449 individuals with expression and protein QTL summary statistics from blood and liver identifies 25 genes causally linked to LDL-C. These include the known SORT1 and ApoE genes as well as PVRL2, located in the APOE locus, for which a causal role in liver was not known. Our results showcase the strength of MR-link for transcriptome-wide causal inferences.