Narrative:

I was working local control and tower controller in charge. Aircraft Y was on final to runway X and aircraft X was ready to depart runway Y. I cleared aircraft X for takeoff and issued a right turn heading 210. The proper heading for the departure was 120; per LOA. I transposed the numbers and missed my error on the readback. After I observed aircraft X start his turn; he began to enter a cloud layer and I switched him to departure. A few moments later; I realized my error upon watching the radar. I issued a traffic call to aircraft Y on approach and he called aircraft X in sight. No TCAS resolution or ca alert were issued for aircraft proximity.I believe the only recommendations I could make to stop this sort of incident from occurring would be to develop standard instrument departures at ZZZ; which I am not sure is feasible. Also; I believe the covid-19 staffing needs to be changed; and more personnel brought back to mitigate the lack of for control positions and lack of oversight. (ZZZ is reverting to a more normal staffing schedule during pay period xx).

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Original NASA ASRS Text

Title: Tower Controller reported inadvertently giving an incorrect heading to a departing aircraft resulting in a conflict with an aircraft on final.

Narrative: I was working Local Control and Tower CIC. Aircraft Y was on final to Runway X and Aircraft X was ready to depart Runway Y. I cleared Aircraft X for takeoff and issued a right turn heading 210. The proper heading for the departure was 120; per LOA. I transposed the numbers and missed my error on the readback. After I observed Aircraft X start his turn; he began to enter a cloud layer and I switched him to departure. A few moments later; I realized my error upon watching the radar. I issued a traffic call to Aircraft Y on approach and he called Aircraft X in sight. No TCAS resolution or CA alert were issued for aircraft proximity.I believe the only recommendations I could make to stop this sort of incident from occurring would be to develop Standard Instrument Departures at ZZZ; which I am not sure is feasible. Also; I believe the COVID-19 staffing needs to be changed; and more personnel brought back to mitigate the lack of for control positions and lack of oversight. (ZZZ is reverting to a more normal staffing schedule during Pay Period XX).

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.