Does the country provide individual online voter registration/polling assignment checks?

Law no. 208/2015 on the election of the Senate and the Chamber of Deputies, as well as the organisation and functioning of the Permanent Electoral Authority

Article 24

24.1 The Electoral Register is a national computer system for the recording and update of the identification data of the Romanian citizens with the right to vote and of the information concerning their assignment to polling stations.

24.2 The Electoral Register functions to ensure the following objectives: a) recording and updating the identification data of the Romanian citizens with the right to vote; b) carrying out the communications set by law concerning the identification data of voters and their assignment to the polling stations; c) assigning the Romanian citizens with the right to vote to the polling stations; d) drawing up the permanent electoral lists; e) carrying out the communications set by law concerning the update of permanent electoral lists.

OSCE/ODIHR Needs Assessment Mission Report, Romania, Parliamentary Elections, 11 December 2016

Voter registration is managed by the Permanent Electoral Authority (PEA), which extracts the electoral register based on a compilation of information from various government authorities, including the National Register of Persons’ Records, maintained by the Ministry of Interior. Since 2014, the PEA has introduced a centralized electronic register as a means to increase list accuracy and prevent multiple entries. […] Voters can verify their records online or in-person.

The voter registration website can be accessed here.