Fluorescent RNA-based biosensors are useful tools for real-time detection of molecules in living cells. These biosensors typically consist of a chromophore-binding aptamer and a target-binding aptamer, whereby the chromophore-binding aptamer is destabilized until a target is captured, which causes a conformational change to permit chromophore binding and an increase in fluorescence. The target-binding region is typically fabricated using known riboswitch motifs, which are already known to have target specificity and undergo structural changes upon binding. However, known riboswitches only exist for a limited number of molecules, significantly constraining biosensor design. To overcome this challenge, we designed a framework for producing mammalian cell-compatible biosensors using aptamers selected from a large random library by Capture-SELEX. As a proof-of-concept, we generated and characterized a fluorescent RNA biosensor against L-dopa, the precursor of several neurotransmitters. Overall, we suggest that this approach will have utility for generating RNA biosensors that can reliably detect custom targets in mammalian cells.