Here's a nice A.I. summary:
A tariff is a tax imposed by a government on the import or export of goods between countries. Tariffs are a type of trade barrier that can:
Raise prices
Reduce the availability of goods and services
Create an economic burden on foreign exporters
Encourage or protect domestic industry
Reduce pressure from foreign competition
Reduce the trade deficit
Help stabilize a market and make prices predictable
Notice that NOT all of those are bad outcomes! The devil is in the details. For instance, if a foreign country is subsidizing the products that its manufacturers export to the US--thus undercutting US prices (and putting American manufacturers at a disadvantage), in an effort to control the U.S. market, a selective tariff against that country/product could be called for.
However, blanket tariffs against a country that exports to the US will almost inevitably raise prices within the US. (And that's not even taking into account the likelihood that the target country will impose its own retaliatory tariffs, hurting US exports.)
Yet it is not a 100% absolute certainty that prices would rise; there might simply be a lot of Americans put out of work, which would reduce demand and prompt the Fed to lower interest rates. We might end up with a recession, but not necessarily (though probably) inflation.