Thoroughly rinse produce and pat dry.
Trim cucumber, halve lengthwise, then cut into half-moons.
If desired, place beef strips in a microwave-safe bowl in a single layer. Microwave until warm, 1-2 minutes.
Spread ranch dressing on tortillas. Top with beef strips, arugula, wonton strips, and cucumber, placing in center of each tortilla. Fold sides of tortilla toward center, then roll bottom edge towards the top, enclosing sides tightly. Bon appétit!