Yes. A lay Buddhist can date, have a girlfriend or boyfriend, marry, or remain single. Buddhism does not require laypeople to be celibate. The main ethical guideline is the third precept, usually understood as refraining from sexual misconduct.

Dating is not forbidden
Buddhist texts do not create a universal rule against romantic relationships. Household life is recognized as a normal path for lay followers, with teachings about duties between partners, parents, children, and friends.
Whether dating is formal, casual, or connected with marriage depends largely on culture and family expectations.
The third precept
Traditional explanations of sexual misconduct commonly include adultery, coercion, exploitation, and relationships that violate serious commitments or protected relationships.
Many modern Buddhist teachers also emphasize informed consent, honesty, respect, and the avoidance of manipulation or abuse.
Attachment and love are not identical
Buddhism warns against craving and possessive attachment, but this does not mean affection or commitment is forbidden. A caring relationship can cultivate generosity, patience, and compassion.
The challenge is to love without treating another person as property or as the sole source of permanent happiness.
Monastic celibacy
Monks and nuns who maintain full ordination live celibately. Their rules should not be applied automatically to lay Buddhists.
A layperson who wants a stricter period of celibacy may choose it voluntarily for retreat or spiritual discipline.
Practical answer
Having a girlfriend is compatible with lay Buddhist life. The ethical question is whether the relationship is honest, consensual, responsible, and free from exploitation and serious harm.