Well before the civil war there have been two Presidents and one Vice-President, who had served as ambassador to Russia, them being John Q. Adams, James Buchanan and George M. Dallas.
What if John Q. Adams, who at the age of 14 in 1783, accompaning Francis Dana as a secretary on a mission to Saint Petersburg, Russia, to obtain recognition of the new United States, stayed in Russia and was appointed the United States Minister to Russia, by his father in March 4, 1797, staying as ambassador until September 22, 1817, 20 years, 6 months and 18 days. Adams was well liked by the Russian Court and often would be met on walks by Tsar Alexander I or the tsar's brother, Grand Duke Nicholas Pavlovich.
During Adam's time as U.S. Secretary of State (1817–1825) he is able to gain the support of the Russians during the Treaty of 1818, to gain land connecting the US mainland to the Russian colony of Alyeska.
When Adams is elected president in 1825, he begins builds closer bonds with Russia, improving trade links between the US to Russia. He signs an alliance with Russia, the second nation, the US have allied with, stating military, finacial and political support.
In 1853, the Crimean War began with the Russians at war with the Ottoman Empire, within days Secretary of State, William L. Marcy, who had only recently dealt with the Turks during the Koszta Affair, stated that America, would support their long standing allies, Russia, in their struggle.
This lead to the British not declaring war on Russia, due to fears of fighting a two front war (Canada and Crimea) while the French prefered their alliance to the American's over the Turks, meaning the war was a fairer fight, resulting in the Treaty of St. Petersburg (1856) that saw Russia influence in the region of the Black Sea increase, with more trade ships being build and protected by the Russian navy resulting in a richer Russia.
I would hope these events would help lead to the North having more support from the Russians, with the South maybe (secretly) helped by the British. But in the long run see a strong capitalist-constitutional-monarchy Russia work well with the even stronger America.
In political cartoons these two nations are depicted as Eagles, with the russian two-headed eagle and the US bald eagle, standing watch over the world, both policing it.