Answer:
One View
No, a wrought iron fence is considered an "ornamental" fence, not a "privacy fence". A privacy fence is characterized by it's height (usually 6' or more) and its opaqueness (non-transparency). Privacy fences are used to block neighbors or passers by from seeing inside the fenced area.
Wrought iron fences, on the other hand, are usually 3-6' tall and have thin pickets. They can provide a certain level of security due to its strength and height, but most likely will be too transparent to provide any level of privacy.
If privacy is what you desire, then vinyl or wood should be your top choices.
A chain link fence can also provide a privacy if used in conjunction with privacy slats. Privacy slats are vinyl or aluminum inserts that are woven into the links of a chain link fence. They also can enhance a chain link fence aesthetically.
Another View
It depends on what you mean by "privacy fence." If you're looking for complete privacy, then no wrought iron, steel or ornamental aluminum would not provide "complete" privacy.
However, you can obtain semi-privacy fencing with ornamental, rust free aluminum because some styles have double the amount of vertical pickets on each fence panel and/or gate.
These types of styles typically have approximately 1.5" between every 2 vertical pickets.
The vertical pickets are extremely close together and yet, at the same time, wind is allowed to pass through. This prevents premature wear and tear unlike other types of fencing and gate systems (i.e. wood or cheap vinyl).