Vector2 pos = ball.position;
Vector2 prevPos = ball.previousPosition; // You'll have to keep track of where the ball was 1 frame ago.

for (int i=0; i<COLLISION_PRECISION; i++)
{
    Vector2 testPos = lerp(prevPos, pos, i/COLLISION_PRECISION);
    if (PointInsideRect(testPos, paddleRect))
    {
        ball.position = testPos;
        // Do any collision reactions
        break;
    }
}