Yes, you may ask an employee to show their identity card when that is necessary to verify their identity, for example when they join and are registered in your personnel administration. But this does not automatically give you the right to copy the card, read it electronically or record all the data visible on it.
Limit yourself to what is needed
Limit yourself to what that purpose requires. In many cases it is enough to check the identity card visually and record only the necessary data.
The card shows more than you need: a photograph, a signature, a card number and, in many member states, a national identification number (in Belgium the rijksregisternummer). Seeing that data is different from recording it. The photograph and the national identification number are data that call for particular care.
The Belgian data protection authority puts it plainly: identification must be necessary and lawful, and the need to identify someone does not by itself justify taking a copy. What you may record is explained in Which data from an employee’s identity card may I record?. Copies follow a rule of their own: Can I keep a copy of an employee’s identity card?
Be transparent about what you do
Explain clearly to the employee why you are checking their identity and which data you record. Then use that data only for the purposes you communicated, such as personnel administration, payroll and mandatory declarations.
If you only need confirmation of identity, do not make a copy.
Legal basis
The check rests on the principles of purpose limitation and data minimisation (Article 5(1)(b) and (c) GDPR), requires a legal basis under Article 6 GDPR, usually performance of the employment contract or a legal obligation, and comes with the information duty of Article 13 GDPR. In addition, national legislation on personnel administration, social documents and social security declarations determines which data an employer actually has to record.
GDPRWise maps your HR processes, from onboarding to offboarding, so you know for every data item why you keep it.