As per the official press release by the ICC:
Mr Vladimir Vladimirovich Putin, born on 7 October 1952, President of the Russian Federation, is allegedly responsible for the war crime of unlawful deportation of population (children) and that of unlawful transfer of population (children) from occupied areas of Ukraine to the Russian Federation (under articles 8(2)(a)(vii) and 8(2)(b)(viii) of the Rome Statute). The crimes were allegedly committed in Ukrainian occupied territory at least from 24 February 2022. There are reasonable grounds to believe that Mr Putin bears individual criminal responsibility for the aforementioned crimes, (i) for having committed the acts directly, jointly with others and/or through others (article 25(3)(a) of the Rome Statute), and (ii) for his failure to exercise control properly over civilian and military subordinates who committed the acts, or allowed for their commission, and who were under his effective authority and control, pursuant to superior responsibility (article 28(b) of the Rome Statute).
The two paragraphs of the Rome Statute that they quote are:
(vii) Unlawful deportation or transfer or unlawful confinement;
(viii) The transfer, directly or indirectly, by the Occupying Power of parts of its own civilian population into the territory it occupies, or the deportation or transfer of all or parts of the population of the occupied territory within or outside this territory
However it seems like all Russia did in this regard is transfer orphans away from the war zone into Russia. They became orphans due to Russia's invasion and that's certainly a valid crime for the ICC to prosecute, but the accusation of "unlawful deportation" seems quite strange. One could reasonably argue that Ukraine isn't exactly in great shape right now and thus orphans would be safer in Russia away from the war. Again, said war was started by Russia but the treatment of orphans doesn't seem to be unreasonable.
So why is the ICC starting out from a very minor crime rather than prosecuting Putin for starting the war in the first place? I presume there's a political reason behind this as it doesn't seem to make much sense from a purely legal standpoint. At least in my book killing tens of thousands Ukrainians and bombing their country is the very first accusation one should start with.