Combining with stem cell factor (SCF) receptor ligand and transmitting the signal from one side of the membrane to the other to initiate a change in cell activity by catalysis of the reaction: ATP + a protein-L-tyrosine = ADP + a protein-L-tyrosine phosphate. Stem cell factor is a cytokine that stimulates mast cell growth and differentiation. [ GOC:signaling GOC:jl http://www.ncbi.nlm.nih.gov/pubmed/10698217 ]