Why weatherproofing is the landlord’s duty
Yes, usually. Water leaking in through windows, exterior walls, or around door frames is generally the landlord's responsibility, because the law requires rentals to be weatherproofed against rain and the elements.
When rain gets in through a window that will not seal, a cracked wall, or failing weatherproofing, the building is not doing its basic job of keeping water out. Repairing seals, flashing, and exterior walls is part of the landlord's duty to maintain effective weather protection.
Left alone, this kind of intrusion stains walls, warps trim, damages belongings, and encourages mold. Report it to your landlord in writing and photograph it during or right after rain, when the water is visible. Do not let a landlord dismiss it as condensation if rain is clearly coming in. If your landlord will not fix water entering through windows or walls, a free review can help you understand your rights.
This is general information about California tenant rights, not legal advice. Every situation is different.