Combine bean, oil, juice, garlic, thyme, salt and pepper in a the bowl of a food processor. Purée until smooth, stopping once to scrape down sides, for bean spread. (Can be made ahead. Cover and chill up to 2 days.)
Spread bean spread on one side of each tortilla, leaving a 1-inch border around edge. Arrange turkey down center of each tortilla; layer with tomato, onion, cheese and arugula. Starting at one end, tightly roll each tortilla and place, seam side down, on a serving plate. Cut crosswise in half and serve with chips, if desired.