Yes, roses can grow in a pot; all it requires is the appropriate plant and some rich soil. Miniature patio roses (bred to remain small), floribunda roses and even climbing or rambler varieties should all thrive when grown in containers; make sure your support system can support its weight though if growing ramblers.
Once you've chosen your plant, be sure to select an appropriately large container. This will enable the roots to spread freely while helping keep soil temperatures cooler and drying out more slowly. Fill your container halfway with loam-based compost like John Innes No. 2 or 3, combined with up to 20% multipurpose or well-rotten mature compost; mix thoroughly so as to minimize air pockets before placing your rose in its new home.
Cover the soil with a thick layer of mulch to retain moisture and insulate roots during winter. Alternatively, if your area experiences harsh frosts, plant in a garden bed at least two USDA Hardiness Zones colder than its growing zone.
Regular watering of roses is vital, and a great way to measure their need for it is the "knuckle test". Insert your finger into the soil until it feels moist but not soggy, then if that area feels wet to touch, add water until its texture changes back. Most roses should also be repotted every 2-3 years since their heavy feeding needs quickly exhaust most potting mixes; when reppotting use new soil or compost to avoid salt accumulation in old mixes.
