Yes, white bordered cards are legal.
From the Magic: The Gathering Tournament Rules (English version):
Players may use any Authorized Game Cards from Magic: The Gathering
expansions, core sets, special sets, supplements, and promotional
printings. Authorized Game Cards are cards that, unaltered, meet the
following conditions:
The card is genuine and published by Wizards of the Coast
It is important to remember that fake Magic cards exist. Usually,
these cards can be identified as fake under scrutiny. If these cards
are found to be in use in a tournament, they should not continue to be
used. Also, the player using the card may not realize that they are
using fake cards, so aside from alerting them that they are using fake
cards and informing them that they must replace them, we, as judges,
should not take further action unless we believe they knew and were
using such cards intentionally.
Also, Tournament Officials do not have the legal authority to
confiscate fake cards and should not attempt to do so. Stopping their
use in the event is sufficient.
The card has a standard Magic back or is a double-faced card, or is a card that is part of a meld pair.
Artist proofs are published by Wizards of the Coast, but do not have a
standard Magic back. They are, therefore, not usable in tournament
play.
The card does not have squared corners.
Collectors’ Edition cards have black borders on the face, but square
corners and a gold border on the back. These are not legal for
tournament use. Also, uncut sheets of cards are sometimes cut for use.
It is important that these cards have the same corners as all other
cards.
The card has non-silver borders.
Cards from Unglued and Unhinged have silver borders with a standard
Magic back. These are not legal for play. Gold bordered cards also
exist, though they do not have a standard Magic back.
The card is not a token card.
Tokens are used to represent objects that don’t exist as normal Magic
cards. While some official tokens exist, it is not required that they
be used during tournament play.
The card is not damaged or modified in a way that might make it marked.
Significantly creased cards can be distinguished from other cards in a
deck, even sleeved. Also, altered cards may be thicker than the other
cards in the deck, depending on the method used to alter the card. If
any cards can be distinguished from the other cards in the deck
without viewing its front face, then those cards are marked and not
legal for tournament play.
The card is otherwise legal for the tournament as defined by the format.
The cards being played in the deck must be printed in a set that is
legal in the format, even if the printing being used is from an
otherwise illegal set. For example, it is okay to use the Stronghold
printing of Mana Leak in Modern even though Stronghold is not a legal
set for use in Modern.