Could poor circulation be the cause of my spider veins?

Not exactly. They aren't due to poor arterial circulation, which would be more concerning. Though causes are numerous, an important one to be aware of is superficial venous insufficiency: increased pressure in leg veins due to faulty vein valves. If such veins are symptomatic or aggregate in certain areas such as the ankle, they may point to an underlying easily treatable condition that may otherwise worsen.
Spider veins. The circulation consists of two parts- the arteries take blood from the heart to the rest of the body and veins return the blood back to the heart. When we refer to poor circulation this refers to the arteries not the veins. The causes of spider veins are many including hereditary, aging, hormones, pregnancies, sun exposure and sometimes weakened venous valves but not poor circulation.
Venous circulation. We inherit 2 things wrong with our veins: weak vein walls and or weak vein valves inside the veins. So you could have spider veins with a medical vein condition called venous insufficiency- a backward flow of venous blood down your legs instead of going up to your heart except when you are lying down. Othertimes, you can just have cosmetic spider veins and can be treated with sclerotherapy.
No. What most people mean when they talk about poor circulation is that blood doesn't flow very well in their arteries. Spider veins are not affected by arteries at all. The problem is with your veins. Although it is possible to have bad arteries and veins, most people aren't that unlucky. Fortunately, it is pretty safe to that nearly everyone with spider veins has normal arterial circulation.
Spider veins. Spider veins most of the time are only a esthetic problem. They don't need to be treated. They are not a sign of "poor circulation".
Spider veins. Spider veins are mostly due to hormonal changes and as such are more common in women Yes they are abnormal but are not a predictor of circulatory disturbance.
Usually not. Although some patients with poor circulation (known as venous insufficiency) develop more extensive spider vein disease on their legs and feet, they also usually have varicose veins and other circulation issues. People with only spider veins, especially younger people like yourself, just have a minor dermatology predisposition to the small skin veins and is does not indicate poor leg circulation.