It's generally (though not universally) accepted that the Soviet Union behaved in the manner of a traditional empire, however calling the Soviet Union 'an empire' is a bit of a loaded statement-- especially in the context of the 20th century when the British Empire and French Colonial Empire were either alive and well or living in the not-so-distant memory of the peoples of the world. Thus, the short answer to this question is yes-- the Soviet Union is (rightly) considered to have been an imperial power but no-- the term "Soviet Empire" is not appropriate to throw around without qualification. I talk about the USSR's transition from its revolutionary origins to a more traditional international actor in this answer which I think provides a good lead-in to the kinds of issues that need to be understood when answering this question, I'd recommend you give it a read-- the following excerpt summarizes the key point though which is this:
[A]t its inception the Soviet Union tried to style itself as a sort of 'post-nation-state' nation-state but was forced to behave more and more like a traditional international actor as time progressed.
There are plenty of examples of the Soviet Union evincing traditional imperialist tendencies, no matter how much they tried to dress it up as Revolutionary Internationalist policy or how loaded the term 'empire' may be. This is a country (or collection of countries) which:
Those are the big ones, and just to be clear-- I'm defining 'imperialism' in the most reasonable way I can here using Harrison M. Wright's guidelines for doing so in his 1967 essay Imperialism: the Word and its Meanings^([)^(1)^(]): the process by which a nation uses military force, coercion, and propaganda to gain territory and influence. If you have a very specific expression of imperialism that you want to understand with respect to Soviet policy, I'm all ears and will try my best to answer any follow-up questions.
If you don't have time to read Wright's whole essay linked above, allow me to summarize: the author talks about the inherent pitfalls of using words like 'imperialism' in the post-imperial modern world when the word has become a pejorative and its meaning has been obscured to the point of near-ambiguity and certainly diminishing returns on any actual substantial definitional power, which is why I'm spelling it out so explicitly-- it doesn't come from a place of condescension or abject pedantry.
All that disclaimed though, this conversation becomes infinitely more interesting when you start asking why the Soviet Union behaved imperially. Here, there are two conflicting schools of thought which I'll personify with Professors Robert Service and Richard Pipes (RIP). Service argues that the impetus for Soviet imperialism lay within communism (and to a lesser extent Marxism) itself and therefore Revolutionary Internationalist policy is an inevitability in any nation which claims to be striving toward those outcomes. Pipes argues that there was something authentically Russian about the expansionary policy of the Soviet Union and the banner of Marxism-Leninism was more like a placeholder than a rallying ideology-- that is, maybe communism was nominally the justification Moscow was using to push its borders further and further west, but in fact, that desire was rooted in Great Russian territorial ambitions to the core.
Neither Service nor Pipes is 100% in either camp-- of course. They are just convenient proponents for each of these respective hypotheses so I've chosen to use them in that manner.
From Pipes' Survival is not Enough (1984):
The decisive factors [for Soviet authoritarianism] are not the ideas but the soil on which they happen to fall.
Compared to a 1993 political opinion piece Service wrote for The Independent:
[T]he Orwellian maxim that he who controls the past also controls the present still holds true. [...] historians who once lauded Lenin now proclaim that he was a mass murderer. The entire Marxist-Leninist experiment is denounced. The blame for all Russia's ills is placed squarely on the Communist Party. [...]
Yeltsin and his supporters are not totalitarian in aspiration; but they recognise that, in Russia's present turmoil, a new identity has somehow to be formed. The main problem is that, until recently, Russians were encouraged to think of themselves as the main constituent segment of 'the Soviet people'. This was Stalin's way of conferring a quasi-imperial role upon them.^([)^(2)^(])
But what about contemporaneously? Both of these historians are looking backward and assessing the events after the fact. Can we know what the Soviets were thinking at the time? Why did they think they were expanding?
At this point, the most valuable contrast to answer this question is the one between Lev Trotsky and Iosef Stalin. Trotsky, the inveterate revolutionary, is going to play the role of Service here (that is, the USSR is expanding to further the cause of worldwide communism) and Stalin, the inveterate pragmatist, is going to be our Pipes (that is, the USSR is expanding to further its superior Russo-centric culture and/or 'protect' Russia proper). I'm going to use the Winter War as the backdrop for this conversation since we can almost all agree that the Soviet invasion of Finland in 1939 was about as pure an act of imperialist expansionism by the Soviet Union that you're going to find (which doesn't seek to belittle the invasions of Poland, Afghanistan, Lithuania, Estonia, Latvia, Georgia, Ukraine, Belarus, Armenia, Azerbaijan, Mongolia, China, Iran, or any others-- I just find this example to be the most fitting for my own purposes here).
From Trotsky's Balance Sheet of the Finnish Events (Trotsky gets a gold star for euphemism on that title):
[T]o approach the question of the fate of small states from the standpoint of 'national independence,' 'neutrality,' etc., is to remain in the sphere of imperialist mythology. The struggle involves world domination. The question of the existence of the USSR will be solved in passing. [...] So far as the small and second rate states are concerned, they are already today pawns in the hands of the great powers. The sole freedom they still retain, and this only to a limited extent, is the freedom of choosing between masters.^([)^(3)^(])
His justification for the invasion of Finland (in which he played no part remember, Trotsky is writing here from exile in Mexico) is, 'well they've got to be someone's lackey so they may as well be ours because communism has the best interests of the working man in mind.' That opinion in and of itself epitomizes the imperialism of 20th century grand narrative: the 'inevitability' of the subordination of small nations to their more powerful neighbors as justification for their subordination to their more powerful neighbors was the generally agreed upon talking point that the great powers used to more or less arbitrarily adjudicate the lines on the map against the will and without the consent of entire nations of people.
