20 amps: the short answer
At 240 V single-phase over 100 feet,
a 20 amps copper load needs 10 AWG (about 2.02% drop). Ampacity alone would allow copper 12 AWG, but over 100 feet voltage drop pushes the recommendation up to 10 AWG to stay within the 3% target (about 2.02%).
Before you pull wire
This recommendation covers ampacity and voltage drop only, for copper at
75 °C. It does not apply ambient-temperature or conductor-count
derating, the 125% factor for continuous loads, conduit fill, or terminal ratings — any of
which can push the size up. Aluminum of the same load typically goes up one or two sizes.
Always confirm with a licensed electrician and your local code (AHJ).
Ampacity per NEC 310.16; voltage drop per NEC Ch.9 Table 8 (75 °C copper).