Heat oil and curry powder in a 2-qt. saucepan over medium heat. Cook, stirring frequently, until curry powder is fragrant, about 2 minutes. Add onion, garlic, and ginger and cook, stirring occasionally, until soft, about 10 minutes.
Add apricots and raisins along with 1 cup water, lime juice, and sugar. Cook, stirring occasionally, until thickened, about 20 minutes.