Do import tariffs tend to increase a country's exchange rate (if so, why)? From Prof. Stiglitz' Vanity Fair article:  


  How, one might ask, is this possible, given Trump’s rhetoric, his
  determination to move against China with a 45 percent tariff? There’s
  a global macroeconomic variable that Trump left out of his calculus,
  and that’s America’s exchange rate—not just with China, but with the
  entire world. If America’s exchange rate increases, our exports become
  more expensive, and imports become cheaper.


He doesn't explicitly say that tariffs tend to increase a country's exchange rate. He leaves it as a standalone conditional. If it's simply a conditional, he could mean that there's a nonzero chance that the Dollar's value will increase independently. However, I felt like maybe he infers some causality. 

I feel like a tariff would change the trade balance such that the US will import less, while exports are fixed.

Do import tariffs tend to increase a country's exchange rate? If so, why?
Suppose that there is no 45 percent tariff and the market is in some kind of equilibrium. That is the demand for yuans equals the supply of yuans at the current exchange rate.

Now assume Trump does impose a 45 percent tariff. This makes imported Chinese goods in the US more expensive for the American consumer. As a result the consumers will buy fewer Chinese import goods. So far they paid for these goods with dollars and the corporation importing the goods used those dollars to buy yuans and pay for the goods. As a result of the decreased import demand the corporation will want less goods and hence it will buy fewer yuans. Thus decreasing the demand for yuans. The currency exchange market is similar to other markets: If at a price (in this instance this is the USD/CNY exchange rate) the supply outstrips demand the price will decrease. This means that the dollar becomes 'stronger', you will have to pay more yuans to get a dollar.

As a result exports do become somewhat more expensive (in yuans) and imports do become somewhat cheaper (in dollars) until an equilibrium is reached on both the currency and the good markets.